sequence_id
stringlengths 7
7
| sequence_name
stringlengths 4
573
| sequence
listlengths 1
348
| keywords
listlengths 1
8
| score
int64 1
2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
int64 0
635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
| filename
stringlengths 29
29
| hash
stringlengths 32
32
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A355301
|
Normal undulating numbers where "undulating" means that the alternate digits go up and down (or down and up) and "normal" means that the absolute differences between two adjacent digits may differ.
|
[
"0",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"10",
"12",
"13",
"14",
"15",
"16",
"17",
"18",
"19",
"20",
"21",
"23",
"24",
"25",
"26",
"27",
"28",
"29",
"30",
"31",
"32",
"34",
"35",
"36",
"37",
"38",
"39",
"40",
"41",
"42",
"43",
"45",
"46",
"47",
"48",
"49",
"50",
"51",
"52",
"53",
"54",
"56",
"57",
"58",
"59",
"60",
"61",
"62",
"63",
"64",
"65",
"67",
"68",
"69",
"70",
"71",
"72",
"73",
"74",
"75",
"76",
"78",
"79",
"80",
"81",
"82",
"83",
"84",
"85",
"86",
"87",
"89",
"90",
"91",
"92",
"93",
"94",
"95",
"96",
"97",
"98",
"101",
"102",
"103",
"104",
"105",
"106",
"107",
"108",
"109",
"120",
"121",
"130",
"131",
"132",
"140",
"141",
"142",
"143",
"150"
] |
[
"nonn",
"base"
] | 44 | 1 | 3 |
[
"A010784",
"A033619",
"A043096",
"A046075",
"A059168",
"A241157",
"A241158",
"A355301",
"A355302",
"A355303",
"A355304"
] | null |
Bernard Schott, Jun 27 2022
| 2024-03-09T09:35:54 |
oeisdata/seq/A355/A355301.seq
|
b7304c6c25abb52f584ed22d00f3d64e
|
A355302
|
a(n) is the number of normal undulating integers that divide n.
|
[
"1",
"2",
"2",
"3",
"2",
"4",
"2",
"4",
"3",
"4",
"1",
"6",
"2",
"4",
"4",
"5",
"2",
"6",
"2",
"6",
"4",
"2",
"2",
"8",
"3",
"4",
"4",
"6",
"2",
"8",
"2",
"6",
"2",
"4",
"4",
"9",
"2",
"4",
"4",
"8",
"2",
"8",
"2",
"3",
"6",
"4",
"2",
"10",
"3",
"6",
"4",
"6",
"2",
"8",
"2",
"8",
"4",
"4",
"2",
"12",
"2",
"4",
"6",
"7",
"4",
"4",
"2",
"6",
"4",
"8",
"2",
"12",
"2",
"4",
"6",
"6",
"2",
"8",
"2",
"10",
"5",
"4",
"2",
"12",
"4",
"4",
"4",
"4",
"2",
"12",
"4",
"6",
"4",
"4",
"4",
"12",
"2",
"6",
"3",
"8"
] |
[
"nonn",
"base"
] | 11 | 1 | 2 |
[
"A355301",
"A355302",
"A355303",
"A355304"
] | null |
Bernard Schott, Jun 29 2022
| 2022-07-07T16:20:28 |
oeisdata/seq/A355/A355302.seq
|
00f38a3be105f2426abc077db5ddbbe4
|
A355303
|
a(n) is the smallest integer that has n normal undulating divisors.
|
[
"1",
"2",
"4",
"6",
"16",
"12",
"64",
"24",
"36",
"48",
"126",
"60",
"320",
"144",
"168",
"120",
"252",
"180",
"560",
"240",
"630",
"420",
"780",
"360",
"1890",
"960",
"1920",
"720",
"1560",
"1080",
"1260",
"1440",
"1680",
"4368",
"2160",
"3240",
"3120",
"3360",
"4320",
"2520",
"6300",
"6120",
"8640",
"6240",
"13104",
"5040",
"12480",
"9360",
"12240",
"7560"
] |
[
"nonn",
"base"
] | 27 | 1 | 2 |
[
"A005179",
"A355301",
"A355302",
"A355303",
"A355304"
] | null |
Bernard Schott, Jun 29 2022
| 2022-07-11T16:10:04 |
oeisdata/seq/A355/A355303.seq
|
9b42a157d7facc5eb8bb409858d0b34f
|
A355304
|
Integers whose number of normal undulating divisors sets a new record.
|
[
"1",
"2",
"4",
"6",
"12",
"24",
"36",
"48",
"60",
"120",
"180",
"240",
"360",
"720",
"1080",
"1260",
"1440",
"1680",
"2160",
"2520",
"5040",
"7560",
"10080",
"15120",
"21840",
"28080",
"32760",
"56160",
"65520",
"98280",
"131040",
"196560",
"393120",
"589680",
"786240",
"1113840",
"1670760",
"2227680",
"3341520",
"6683040",
"13366080",
"20049120"
] |
[
"nonn",
"base"
] | 24 | 1 | 2 |
[
"A002182",
"A046952",
"A053624",
"A093036",
"A181808",
"A340548",
"A340549",
"A350756",
"A355301",
"A355302",
"A355303",
"A355304"
] | null |
Bernard Schott, Jun 30 2022
| 2022-07-07T16:20:17 |
oeisdata/seq/A355/A355304.seq
|
996741f696a525679dc18ca3459705db
|
A355305
|
Carmichael numbers ending in 5.
|
[
"1105",
"2465",
"10585",
"62745",
"278545",
"449065",
"825265",
"1050985",
"2531845",
"3224065",
"3664585",
"5632705",
"6054985",
"9582145",
"11119105",
"12945745",
"13187665",
"13992265",
"15403285",
"21584305",
"22665505",
"28787185",
"31692805",
"36121345",
"37354465",
"39353665",
"40280065",
"41298985",
"47006785",
"60112885",
"67371265",
"74165065",
"84417985"
] |
[
"nonn",
"base"
] | 22 | 1 | 1 |
[
"A002997",
"A017329",
"A352970",
"A354609",
"A355305",
"A355307",
"A355309"
] | null |
Omar E. Pol, Jul 03 2022
| 2022-07-26T10:10:13 |
oeisdata/seq/A355/A355305.seq
|
82d352cb536a9d29bc0236be4a400bd1
|
A355306
|
Number of partitions of n in which the number of prime parts is not equal to the number of nonprime parts.
|
[
"0",
"1",
"2",
"2",
"4",
"7",
"8",
"13",
"19",
"25",
"38",
"48",
"65",
"91",
"120",
"153",
"209",
"264",
"343",
"443",
"563",
"713",
"912",
"1133",
"1428",
"1789",
"2217",
"2746",
"3406",
"4178",
"5139",
"6296",
"7670",
"9344",
"11360",
"13732",
"16612",
"20038",
"24078",
"28915",
"34660",
"41402",
"49439",
"58887",
"69983",
"83088",
"98476",
"116436",
"137589",
"162244",
"191018"
] |
[
"nonn"
] | 27 | 0 | 3 |
[
"A000040",
"A000041",
"A000607",
"A002095",
"A002096",
"A018252",
"A155515",
"A355158",
"A355225",
"A355306"
] | null |
Omar E. Pol, Jun 28 2022
| 2022-07-16T17:16:42 |
oeisdata/seq/A355/A355306.seq
|
6769bb5fe6396a325b9106cf0a5262ad
|
A355307
|
Carmichael numbers ending in 7.
|
[
"46657",
"126217",
"748657",
"1569457",
"4909177",
"9613297",
"11972017",
"40160737",
"55462177",
"65037817",
"106041937",
"161035057",
"178451857",
"193910977",
"196358977",
"311388337",
"328573477",
"338740417",
"358940737",
"403043257",
"461502097",
"499310197",
"556450777",
"569332177",
"633639097",
"784966297",
"902645857",
"981789337",
"1125038377"
] |
[
"nonn",
"base"
] | 24 | 1 | 1 |
[
"A002997",
"A017353",
"A352970",
"A354609",
"A355305",
"A355307",
"A355309"
] | null |
Omar E. Pol, Jul 24 2022
| 2022-07-25T15:41:37 |
oeisdata/seq/A355/A355307.seq
|
78fd4d63d8c5f291c43214d234e647eb
|
A355308
|
Expansion of e.g.f. -LambertW(x^3/6 * (1 - exp(x))).
|
[
"0",
"0",
"0",
"0",
"4",
"10",
"20",
"35",
"1176",
"10164",
"58920",
"277365",
"4472380",
"69189406",
"772011604",
"6861855455",
"95279504880",
"1819310613800",
"30768119885136",
"430200439251369",
"6770486332450740",
"139958614722287410",
"3033142442978720380",
"58782387380290683571",
"1138026666874389737544"
] |
[
"nonn"
] | 16 | 0 | 5 |
[
"A048802",
"A353999",
"A355180",
"A355181",
"A355308",
"A357267"
] | null |
Seiichi Manyama, Sep 24 2022
| 2025-02-16T08:34:03 |
oeisdata/seq/A355/A355308.seq
|
d1ddc752b3cb3ee37b6eaa301f7ea7c3
|
A355309
|
Carmichael numbers ending in 3.
|
[
"52633",
"63973",
"334153",
"670033",
"997633",
"2508013",
"2628073",
"5968873",
"6733693",
"13696033",
"15829633",
"15888313",
"18900973",
"26280073",
"27336673",
"46483633",
"53711113",
"65241793",
"67653433",
"75765313",
"124630273",
"133344793",
"158864833",
"182356993",
"227752993",
"242641153",
"292244833",
"426821473",
"577240273",
"580565233",
"600892993"
] |
[
"nonn",
"base"
] | 18 | 1 | 1 |
[
"A002997",
"A017305",
"A352970",
"A354609",
"A355305",
"A355307",
"A355309"
] | null |
Omar E. Pol, Jul 25 2022
| 2022-07-26T13:38:53 |
oeisdata/seq/A355/A355309.seq
|
c3ad670fbdb0851a4b7b7a5aa1313ebb
|
A355310
|
Total number of V-toothpicks after n-th stage in a cellular automaton with V-toothpicks of 60 degrees (see Comments lines for precise definition).
|
[
"0",
"1",
"3",
"7",
"13",
"21",
"27",
"37",
"51",
"69",
"79",
"89",
"103",
"123",
"141",
"165",
"201",
"245",
"267"
] |
[
"nonn",
"more"
] | 80 | 0 | 3 |
[
"A139250",
"A153006",
"A160120",
"A161206",
"A161412",
"A161420",
"A299476",
"A299478",
"A327330",
"A327332",
"A355310",
"A355311"
] | null |
Jean Hoffmann and Omar E. Pol, Jul 20 2022
| 2022-08-31T09:12:31 |
oeisdata/seq/A355/A355310.seq
|
fa25036c1d1ce15f4594ce71ec3b6142
|
A355311
|
Number of V-toothpicks added at n-th stage to the V-toothpick structure of A355310.
|
[
"1",
"2",
"4",
"6",
"8",
"6",
"10",
"14",
"18",
"10",
"10",
"14",
"20",
"18",
"24",
"36",
"44",
"22"
] |
[
"nonn",
"tabf",
"more"
] | 27 | 1 | 2 |
[
"A011782",
"A139251",
"A160121",
"A161207",
"A161413",
"A161421",
"A296612",
"A299477",
"A299479",
"A355310",
"A355311"
] | null |
Jean Hoffmann and Omar E. Pol, Jul 20 2022
| 2022-08-31T09:08:06 |
oeisdata/seq/A355/A355311.seq
|
72c869e95a0819332ed9cf5a2f927e95
|
A355312
|
Irregular triangle read by rows, in which the rows list groups of consecutive integers taking the same number of halving and tripling steps to reach 1 in '3X+1' problem. Groups are in order of the number of steps required, and in numerical order among those with the same number of steps.
|
[
"20",
"21",
"12",
"13",
"84",
"85",
"52",
"53",
"340",
"341",
"34",
"35",
"212",
"213",
"226",
"227",
"1364",
"1365",
"68",
"69",
"70",
"452",
"453",
"454",
"22",
"23",
"140",
"141",
"150",
"151",
"852",
"853",
"908",
"909",
"5460",
"5461",
"44",
"45",
"46",
"276",
"277",
"300",
"301",
"302",
"1812",
"1813",
"14",
"15",
"92",
"93",
"564",
"565",
"604",
"605",
"3412",
"3413"
] |
[
"nonn",
"tabf"
] | 42 | 1 | 1 |
[
"A006577",
"A078417",
"A127824",
"A355312"
] | null |
Paul Duckett, Jun 27 2022
| 2022-07-12T08:39:52 |
oeisdata/seq/A355/A355312.seq
|
0fa1b06310ed505dfb64e5c57b402067
|
A355313
|
Numbers that can be written as reversals in two different bases, where the bases are also reversals. (Trailing zeros are allowed.)
|
[
"65",
"67",
"75",
"85",
"96",
"130",
"134",
"150",
"170",
"192",
"195",
"225",
"255",
"288",
"300",
"327",
"340",
"375",
"381",
"425",
"433",
"443",
"450",
"456",
"487",
"510",
"525",
"595",
"600",
"654",
"665",
"667",
"675",
"680",
"750",
"762",
"765",
"795",
"825",
"886",
"895",
"900",
"912",
"927",
"974",
"975",
"981",
"996",
"1050",
"1125",
"1139",
"1200",
"1275",
"1277",
"1308",
"1330",
"1334",
"1340",
"1350",
"1368",
"1535",
"1543",
"1590"
] |
[
"nonn",
"base"
] | 26 | 1 | 1 |
[
"A354474",
"A355313"
] | null |
Jordan Canevari, Jun 27 2022
| 2022-08-23T10:37:07 |
oeisdata/seq/A355/A355313.seq
|
469f7e577fc77bc1cb650900da7efa94
|
A355314
|
Lexicographically earliest sequence of positive integers on a square spiral such that the difference between all orthogonally adjacent pairs of numbers is distinct.
|
[
"0",
"0",
"1",
"3",
"7",
"12",
"1",
"7",
"15",
"1",
"10",
"23",
"0",
"17",
"35",
"54",
"0",
"27",
"48",
"72",
"0",
"26",
"55",
"83",
"31",
"0",
"34",
"69",
"106",
"39",
"1",
"41",
"83",
"126",
"1",
"45",
"91",
"140",
"77",
"128",
"2",
"57",
"1",
"61",
"119",
"183",
"1",
"93",
"158",
"1",
"74",
"143",
"218",
"0",
"115",
"192",
"0",
"79",
"160",
"244",
"2",
"87",
"174",
"1",
"89",
"185",
"1",
"166",
"6",
"101",
"198",
"296",
"0",
"101",
"203",
"1"
] |
[
"nonn"
] | 11 | 0 | 4 |
[
"A274640",
"A275609",
"A307834",
"A355270",
"A355314"
] | null |
Scott R. Shannon, Jun 28 2022
| 2022-08-09T06:47:27 |
oeisdata/seq/A355/A355314.seq
|
320755e046dbb2a65c176a30714e0ae5
|
A355315
|
Triangular array read by rows: T(n,k) is the number of independent collections of subsets of [n] having exactly k members, n>=0, 0<=k<=A347025(n).
|
[
"1",
"1",
"1",
"1",
"3",
"3",
"1",
"7",
"21",
"26",
"6",
"1",
"15",
"105",
"400",
"803",
"782",
"340",
"34"
] |
[
"nonn",
"tabf",
"more"
] | 19 | 0 | 5 |
[
"A000012",
"A000225",
"A102896",
"A134057",
"A355315"
] | null |
Geoffrey Critzer, Jun 28 2022
| 2023-01-16T14:56:02 |
oeisdata/seq/A355/A355315.seq
|
d02e4648b3a49fd6bc46525db21c4eb0
|
A355316
|
Stuttering Look and Say sequence with seed 0.
|
[
"0",
"10",
"1110",
"333110",
"333322110",
"4444322222110",
"444441355555222110",
"5555541113555555333222110",
"5555551433311366666653333333222110",
"6666665111433332211366666661577777773333222110",
"66666661533311444443222221137777777611157777777744443333222110"
] |
[
"base",
"nonn"
] | 27 | 1 | 2 |
[
"A001155",
"A014715",
"A355316"
] | null |
Jonathan Comes, Jun 28 2022
| 2022-08-30T16:08:05 |
oeisdata/seq/A355/A355316.seq
|
416bff355cc6113c6a35761c2ab10093
|
A355317
|
Prime numbers that have the same base-10 digits as their prime index (with multiplicity), disregarding zero digits.
|
[
"5701",
"27091",
"50417",
"55049",
"57089",
"60601",
"61051",
"63607",
"66301",
"72019",
"132607",
"270913",
"284057",
"574031",
"654301",
"936007",
"936907",
"950647",
"1250609",
"1461001",
"1504417",
"1580921",
"1682069",
"1703287",
"1750631",
"1810553",
"1810573",
"1837601",
"2050241",
"2145089",
"2485001",
"2641109",
"2709169",
"2800333",
"2805703"
] |
[
"base",
"easy",
"nonn"
] | 48 | 1 | 1 |
[
"A355317",
"A355318",
"A355418",
"A355539"
] | null |
Xiaofeng Wang, Jun 28 2022
| 2022-07-07T08:03:42 |
oeisdata/seq/A355/A355317.seq
|
667bfdabb5dfbfa07fc251fd27945b17
|
A355318
|
Indices of the primes that have the same base-10 digits as the corresponding prime number (with multiplicity), disregarding zero digits.
|
[
"751",
"2971",
"5174",
"5594",
"5789",
"6106",
"6151",
"6376",
"6613",
"7129",
"12376",
"23719",
"24758",
"47135",
"53146",
"73906",
"73969",
"74956",
"96512",
"111406",
"114475",
"119825",
"126896",
"128377",
"131657",
"135815",
"135817",
"137681",
"152402",
"158924",
"182045",
"192641",
"197269",
"203383",
"203758",
"215809",
"218332",
"230261",
"230431",
"232946",
"233485",
"235918"
] |
[
"base",
"easy",
"nonn"
] | 29 | 1 | 1 |
[
"A355317",
"A355318",
"A355539"
] | null |
Xiaofeng Wang, Jun 28 2022
| 2022-07-07T08:03:33 |
oeisdata/seq/A355/A355318.seq
|
36152433c6a3e7ebb4a8ef9d1566f452
|
A355319
|
Maximal GCD of four positive integers with sum n.
|
[
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"3",
"4",
"1",
"3",
"1",
"5",
"3",
"2",
"1",
"6",
"5",
"2",
"3",
"7",
"1",
"6",
"1",
"8",
"3",
"2",
"7",
"9",
"1",
"2",
"3",
"10",
"1",
"7",
"1",
"11",
"9",
"2",
"1",
"12",
"7",
"10",
"3",
"13",
"1",
"9",
"11",
"14",
"3",
"2",
"1",
"15",
"1",
"2",
"9",
"16",
"13",
"11",
"1",
"17",
"3",
"14",
"1",
"18",
"1",
"2",
"15",
"19",
"11",
"13",
"1",
"20",
"9",
"2",
"1",
"21",
"17",
"2",
"3",
"22",
"1",
"18",
"13",
"23",
"3",
"2",
"19",
"24",
"1",
"14",
"11",
"25"
] |
[
"nonn"
] | 24 | 4 | 5 |
[
"A008233",
"A032742",
"A129649",
"A354598",
"A354599",
"A354601",
"A355249",
"A355319",
"A355366",
"A355368",
"A355402"
] | null |
Wesley Ivan Hurt, Jun 29 2022
| 2022-09-21T11:27:45 |
oeisdata/seq/A355/A355319.seq
|
258519ab58854b3bcdb9ea278a8817e4
|
A355320
|
Irregular triangle T(n, k), n >= 0, -2*n <= k <= 2*n, read by rows; T(0, 0) = 1; for n > 0, T(n, k) is the sum of all terms in previous rows at one knight's move away.
|
[
"1",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"2",
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"2",
"3",
"2",
"0",
"2",
"3",
"2",
"0",
"0",
"1",
"1",
"0",
"0",
"3",
"4",
"3",
"1",
"6",
"8",
"6",
"1",
"3",
"4",
"3",
"0",
"0",
"1",
"1",
"0",
"0",
"4",
"5",
"4",
"3",
"12",
"16",
"12",
"6",
"12",
"16",
"12",
"3",
"4",
"5",
"4",
"0",
"0",
"1",
"1",
"0",
"0",
"5",
"6",
"5",
"6",
"20",
"27",
"21",
"18",
"33",
"44",
"33",
"18",
"21",
"27",
"20",
"6",
"5",
"6",
"5",
"0",
"0",
"1"
] |
[
"nonn",
"tabf",
"nice",
"look"
] | 22 | 0 | 11 |
[
"A002605",
"A096608",
"A096609",
"A096610",
"A096611",
"A096612",
"A355320",
"A355339"
] | null |
Rémy Sigrist, Jun 28 2022
| 2023-05-13T08:27:01 |
oeisdata/seq/A355/A355320.seq
|
d27971331a7850ae8cdc9470d5733303
|
A355321
|
Numbers k such that the k-th composition in standard order has the same number of even parts as odd.
|
[
"0",
"5",
"6",
"17",
"18",
"20",
"24",
"43",
"45",
"46",
"53",
"54",
"58",
"65",
"66",
"68",
"72",
"80",
"96",
"139",
"141",
"142",
"149",
"150",
"154",
"163",
"165",
"166",
"169",
"172",
"177",
"178",
"180",
"184",
"197",
"198",
"202",
"209",
"210",
"212",
"216",
"226",
"232",
"257",
"258",
"260",
"264",
"272",
"288",
"320",
"343",
"347",
"349",
"350",
"363",
"365"
] |
[
"nonn"
] | 7 | 1 | 2 |
[
"A000069",
"A000712",
"A001405",
"A001969",
"A026424",
"A028260",
"A045931",
"A047993",
"A098123",
"A106529",
"A108949",
"A108950",
"A130780",
"A171966",
"A239241",
"A240009",
"A241638",
"A242498",
"A242821",
"A277579",
"A325698",
"A325700",
"A349157",
"A352129",
"A355321"
] | null |
Gus Wiseman, Jun 28 2022
| 2022-06-30T08:40:55 |
oeisdata/seq/A355/A355321.seq
|
23f5e873ac7c6cfcc1ec93d96253a0b7
|
A355322
|
LCM of Lucas numbers {L(1), L(2), ..., L(n)}.
|
[
"1",
"3",
"12",
"84",
"924",
"2772",
"80388",
"3778236",
"71786484",
"2943245844",
"585705922956",
"13471236227988",
"7018514074781748",
"1972202455013671188",
"61138276105423806828",
"134932175364670341669396",
"481842798227237790101413116",
"154671538230943330622553610236"
] |
[
"nonn",
"easy"
] | 26 | 1 | 2 |
[
"A000032",
"A035105",
"A062954",
"A355322"
] | null |
Clark Kimberling, Jul 16 2022
| 2024-09-26T17:36:54 |
oeisdata/seq/A355/A355322.seq
|
3893bdb8e3d857f64c4bff2c4a74658b
|
A355323
|
Numbers k such that A007063(k) = A356026(k).
|
[
"1",
"2",
"3",
"371",
"5131",
"9250",
"26664"
] |
[
"nonn",
"more",
"hard"
] | 6 | 1 | 2 |
[
"A007063",
"A355323",
"A356026"
] | null |
Clark Kimberling, Jul 25 2022
| 2023-01-26T02:15:28 |
oeisdata/seq/A355/A355323.seq
|
ccaacff62dcde418babcc4df7ac00026
|
A355324
|
Lower midsequence of the Fibonacci numbers (1,2,3,5,8,...) and Lucas numbers (1,3,4,7,11,...); see Comments.
|
[
"1",
"2",
"3",
"6",
"9",
"15",
"25",
"40",
"65",
"106",
"171",
"277",
"449",
"726",
"1175",
"1902",
"3077",
"4979",
"8057",
"13036",
"21093",
"34130",
"55223",
"89353",
"144577",
"233930",
"378507",
"612438",
"990945",
"1603383",
"2594329",
"4197712",
"6792041",
"10989754",
"17781795",
"28771549",
"46553345",
"75324894",
"121878239"
] |
[
"nonn",
"easy"
] | 24 | 0 | 2 |
[
"A000032",
"A000045",
"A116470",
"A355324",
"A355325"
] | null |
Clark Kimberling, Jul 16 2022
| 2022-08-08T16:08:57 |
oeisdata/seq/A355/A355324.seq
|
179f05a63bb0a860c3c6b0cde310c199
|
A355325
|
Upper midsequence of the Fibonacci numbers (1,2,3,5,8,...) and Lucas numbers (1,3,4,7,11,...); see Comments.
|
[
"1",
"3",
"4",
"6",
"10",
"16",
"25",
"41",
"66",
"106",
"172",
"278",
"449",
"727",
"1176",
"1902",
"3078",
"4980",
"8057",
"13037",
"21094",
"34130",
"55224",
"89354",
"144577",
"233931",
"378508",
"612438",
"990946",
"1603384",
"2594329",
"4197713",
"6792042",
"10989754",
"17781796",
"28771550",
"46553345",
"75324895",
"121878240"
] |
[
"nonn",
"easy"
] | 16 | 0 | 2 |
[
"A000032",
"A000045",
"A116470",
"A355324",
"A355325"
] | null |
Clark Kimberling, Jul 16 2022
| 2022-07-22T20:52:17 |
oeisdata/seq/A355/A355325.seq
|
9bb2e8c1b2ef02e879ea7c222cc63165
|
A355326
|
Determinant of the n X n matrix [(i-j)^3+d(i,j)]_{1<=i,j<=n}, where d(i,j) is 1 or 0 according as i = j or not.
|
[
"1",
"2",
"67",
"2157",
"96471",
"2312410",
"32099453",
"302049265",
"2134677349",
"12111035146",
"57724828943",
"238763085133",
"877863236043",
"2922096754578",
"8932649551321",
"25364746314689",
"67523106652585",
"169800639240178",
"405912148130875",
"927335183703821",
"2033820866612767",
"4298718682928682",
"8785487346560277",
"17412229912018801",
"33551232473687501"
] |
[
"nonn"
] | 17 | 1 | 2 |
[
"A000578",
"A079034",
"A355175",
"A355326"
] | null |
Zhi-Wei Sun, Jun 28 2022
| 2022-06-29T13:41:07 |
oeisdata/seq/A355/A355326.seq
|
d76e276df4ee0702e0bfd34be65387cd
|
A355327
|
Number of ways to tile a 2 X n board with squares and dominoes where vertical dominoes are only allowed in even-numbered locations.
|
[
"1",
"1",
"5",
"10",
"39",
"83",
"317",
"678",
"2585",
"5531",
"21085",
"45116",
"171987",
"368005",
"1402873",
"3001764",
"11443033",
"24484957",
"93339173",
"199720270",
"761354199",
"1629089495",
"6210256613",
"13288248522",
"50656169297",
"108390330503"
] |
[
"nonn",
"easy"
] | 14 | 0 | 3 |
[
"A030186",
"A355327"
] | null |
Greg Dresden and Zijie He, Jun 28 2022
| 2022-07-01T12:20:29 |
oeisdata/seq/A355/A355327.seq
|
46496d06f6b0d5982f5409603d5b67c6
|
A355328
|
Decimal expansion of the number whose binary expansion differs from its decimal expansion only in the first digit.
|
[
"1",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"1",
"1",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"0",
"0",
"0",
"0",
"1",
"0",
"0",
"1",
"0",
"1",
"1",
"0",
"1",
"1",
"0",
"1",
"0",
"0",
"0",
"1",
"1",
"0",
"0",
"1",
"0",
"0",
"1",
"1",
"0",
"1",
"1",
"1",
"0",
"0",
"0",
"1",
"0",
"1"
] |
[
"nonn",
"cons"
] | 26 | 0 | 1 |
[
"A352677",
"A355328"
] | null |
Leonid Broukhis, Jun 29 2022
| 2022-07-07T02:01:00 |
oeisdata/seq/A355/A355328.seq
|
34f4b32288640eba65dae304da1bd00c
|
A355329
|
Least increasing sequence of primes such that a(n) - 1 is a multiple of 6*n.
|
[
"7",
"13",
"19",
"73",
"151",
"181",
"211",
"241",
"271",
"421",
"463",
"577",
"859",
"1009",
"1171",
"1249",
"1327",
"1621",
"2053",
"2161",
"2269",
"2377",
"3037",
"3169",
"3301",
"3433",
"3727",
"4201",
"5569",
"5581",
"5953",
"6337",
"6733",
"7549",
"7561",
"7993",
"9103",
"9349",
"9829",
"10321",
"10333",
"10837",
"11353",
"11617",
"12421",
"12697",
"12973",
"13249",
"14407",
"15601"
] |
[
"nonn"
] | 13 | 1 | 1 |
[
"A070850",
"A355329"
] | null |
J. M. Bergot and Robert Israel, Jun 29 2022
| 2022-07-05T06:17:03 |
oeisdata/seq/A355/A355329.seq
|
2e168f7eb78f4e591afb4887792514c9
|
A355330
|
Numbers k such that A020696(2^k-1) < A020696(2^k+1).
|
[
"1",
"2",
"3",
"5",
"7",
"9",
"11",
"13",
"15",
"17",
"19",
"21",
"23",
"25",
"26",
"27",
"29",
"31",
"33",
"34",
"35",
"37",
"38",
"41",
"45",
"46",
"47",
"49",
"51",
"53",
"57",
"59",
"61",
"62",
"65",
"67",
"69",
"71",
"73",
"77",
"78",
"81",
"83",
"85",
"89",
"91",
"93",
"95",
"97",
"98",
"99",
"101",
"103",
"105",
"107",
"109",
"111",
"113",
"115",
"118",
"121",
"122",
"123",
"125"
] |
[
"nonn"
] | 9 | 1 | 2 |
[
"A000043",
"A000668",
"A020696",
"A355330"
] | null |
Amiram Eldar, Jun 29 2022
| 2022-06-30T08:36:36 |
oeisdata/seq/A355/A355330.seq
|
3328d525e7757a731d0392bb0c0808a5
|
A355331
|
Numbers k that divide A020696(k).
|
[
"1",
"2",
"6",
"12",
"20",
"24",
"42",
"60",
"72",
"84",
"90",
"120",
"126",
"140",
"144",
"156",
"168",
"180",
"210",
"216",
"220",
"240",
"252",
"280",
"312",
"336",
"342",
"360",
"420",
"432",
"440",
"462",
"468",
"480",
"504",
"540",
"560",
"600",
"624",
"630",
"660",
"672",
"684",
"700",
"720",
"770",
"780",
"816",
"840",
"864",
"880",
"900",
"924",
"936",
"945",
"960",
"990"
] |
[
"nonn"
] | 19 | 1 | 2 |
[
"A020696",
"A355331",
"A355332"
] | null |
Amiram Eldar, Jun 29 2022
| 2022-07-01T05:20:24 |
oeisdata/seq/A355/A355331.seq
|
84bcbc4ee8f1ec846f35befa083d95dc
|
A355332
|
Numbers k such that k | A020696(k) and (k+1) | A020696(k+1).
|
[
"1",
"201824",
"227799",
"313599",
"395199",
"544824",
"638000",
"654975",
"799799",
"862784",
"1056159",
"1204280",
"1269729",
"1447550",
"1890944",
"2276351",
"2460975",
"2481115",
"2781999",
"2821272",
"3348224",
"3382379",
"3403700",
"3832191",
"3864575",
"3956120",
"5142500",
"5961950",
"6116175",
"6401024",
"7050120"
] |
[
"nonn"
] | 17 | 1 | 2 |
[
"A020696",
"A355331",
"A355332"
] | null |
Amiram Eldar, Jun 29 2022
| 2023-10-12T07:45:49 |
oeisdata/seq/A355/A355332.seq
|
1f5a2981095bdcaa7e7b00fb50bfe666
|
A355333
|
Triangle read by rows: T(n,k) is the number of n X n Boolean matrices with Schein rank k, 0 <= k <= n.
|
[
"1",
"1",
"1",
"1",
"9",
"6",
"1",
"49",
"306",
"156",
"1",
"225",
"8550",
"40656",
"16104",
"1",
"961",
"194850",
"5771100",
"21165720",
"6421800"
] |
[
"nonn",
"tabl",
"more"
] | 9 | 0 | 5 |
[
"A002416",
"A064230",
"A286331",
"A354741",
"A355333",
"A355334"
] | null |
Pontus von Brömssen, Jun 29 2022
| 2022-08-22T03:59:40 |
oeisdata/seq/A355/A355333.seq
|
8dccb23ad96c82d8ab1fe83218b687be
|
A355334
|
Triangle read by rows: T(n,k) is the number of unlabeled graphs with n nodes and bipartite dimension (or biclique covering number) k, 0 <= k < n.
|
[
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"4",
"6",
"0",
"1",
"6",
"20",
"7",
"0",
"1",
"9",
"61",
"80",
"5",
"0",
"1",
"12",
"159",
"650",
"221",
"1",
"0",
"1",
"16",
"381",
"4710",
"6866",
"372",
"0",
"0",
"1",
"20",
"832",
"29921",
"183618",
"59950",
"326",
"0",
"0"
] |
[
"nonn",
"tabl",
"more"
] | 5 | 1 | 5 |
[
"A000012",
"A000088",
"A002620",
"A355333",
"A355334",
"A355335",
"A355336"
] | null |
Pontus von Brömssen, Jun 29 2022
| 2022-07-02T14:36:48 |
oeisdata/seq/A355/A355334.seq
|
b9ba7e60e2e66dcfbad8fb0ef9a7a656
|
A355335
|
Triangle read by rows: T(n,k) is the number of unlabeled connected graphs with n nodes and bipartite dimension (or biclique covering number) k, 0 <= k < n.
|
[
"1",
"0",
"1",
"0",
"1",
"1",
"0",
"2",
"4",
"0",
"0",
"2",
"13",
"6",
"0",
"0",
"3",
"38",
"67",
"4",
"0",
"0",
"3",
"94",
"550",
"205",
"1",
"0",
"0",
"4",
"214",
"3996",
"6543",
"360",
"0",
"0",
"0",
"4",
"441",
"25037",
"176012",
"59266",
"320",
"0",
"0"
] |
[
"nonn",
"tabl",
"more"
] | 5 | 1 | 8 |
[
"A001349",
"A004526",
"A355334",
"A355335",
"A355336"
] | null |
Pontus von Brömssen, Jun 29 2022
| 2022-07-02T14:37:04 |
oeisdata/seq/A355/A355335.seq
|
2ea5cf63b431531f5edba56d4bb5c344
|
A355336
|
Number of unlabeled n-node graphs with the largest possible bipartite dimension (or biclique covering number).
|
[
"1",
"1",
"1",
"6",
"7",
"5",
"1",
"372",
"326"
] |
[
"nonn",
"more"
] | 11 | 1 | 4 |
[
"A057359",
"A355334",
"A355335",
"A355336"
] | null |
Pontus von Brömssen, Jun 29 2022
| 2022-07-02T14:37:34 |
oeisdata/seq/A355/A355336.seq
|
bf4b841a01c2b222334c2c82a967a3e2
|
A355337
|
Expansion of e.g.f.: exp(exp(x) + x^2 - 1).
|
[
"1",
"1",
"4",
"11",
"51",
"212",
"1133",
"6001",
"36508",
"228435",
"1559575",
"11079180",
"83753497",
"659858617",
"5459331036",
"46980355355",
"421272977267",
"3917446787884",
"37766791690501",
"376447420971545",
"3875957531387172",
"41149332371734371",
"449984429580538407",
"5061923434006018612",
"58517321729774406129"
] |
[
"nonn"
] | 32 | 0 | 3 |
[
"A000110",
"A277381",
"A316778",
"A355337",
"A355338"
] | null |
Vaclav Kotesovec, Jun 29 2022
| 2024-06-17T15:51:33 |
oeisdata/seq/A355/A355337.seq
|
63567003edda29f047b1419021ebf584
|
A355338
|
Expansion of e.g.f.: exp(exp(x) - x^2 - 1).
|
[
"1",
"1",
"0",
"-1",
"3",
"12",
"-7",
"-47",
"332",
"1347",
"-2105",
"-4200",
"135457",
"474697",
"-900832",
"4682135",
"126196787",
"439488524",
"233313817",
"19129265609",
"239146712732",
"1104038984091",
"5891696027079",
"89831511761320",
"911995655018817",
"6253185308181553",
"54873149768926624",
"653039078246798383"
] |
[
"sign"
] | 17 | 0 | 5 |
[
"A000296",
"A277381",
"A316778",
"A355337",
"A355338"
] | null |
Vaclav Kotesovec, Jun 29 2022
| 2022-06-29T10:15:06 |
oeisdata/seq/A355/A355338.seq
|
675b4ab15ae1017cb030dee9fecf63f5
|
A355339
|
a(n) is the number of central even terms in the n-th row of triangle A355320; a(0) = 0.
|
[
"0",
"3",
"1",
"3",
"3",
"7",
"1",
"3",
"5",
"3",
"5",
"11",
"3",
"11",
"1",
"3",
"5",
"7",
"7",
"3",
"5",
"7",
"9",
"19",
"7",
"3",
"5",
"19",
"3",
"11",
"1",
"3",
"5",
"7",
"9",
"11",
"13",
"11",
"7",
"3",
"5",
"7",
"9",
"11",
"13",
"15",
"17",
"35",
"15",
"11",
"7",
"3",
"5",
"7",
"9",
"35",
"7",
"3",
"5",
"19",
"3",
"11",
"1",
"3",
"5",
"7",
"9",
"11",
"13",
"15",
"17",
"19",
"21",
"23",
"23",
"19",
"15"
] |
[
"nonn"
] | 10 | 0 | 2 |
[
"A000918",
"A355320",
"A355339"
] | null |
Rémy Sigrist, Jun 29 2022
| 2022-06-29T10:31:57 |
oeisdata/seq/A355/A355339.seq
|
a0ecfd3202e3c04559308e9163ec60af
|
A355340
|
a(0) = 0; for n >= 1, a(n) = a(n-1) XOR A001511(n), where XOR denotes bitwise exclusive-or (A003987) and A001511 is the binary ruler function.
|
[
"0",
"1",
"3",
"2",
"1",
"0",
"2",
"3",
"7",
"6",
"4",
"5",
"6",
"7",
"5",
"4",
"1",
"0",
"2",
"3",
"0",
"1",
"3",
"2",
"6",
"7",
"5",
"4",
"7",
"6",
"4",
"5",
"3",
"2",
"0",
"1",
"2",
"3",
"1",
"0",
"4",
"5",
"7",
"6",
"5",
"4",
"6",
"7",
"2",
"3",
"1",
"0",
"3",
"2",
"0",
"1",
"5",
"4",
"6",
"7",
"4",
"5",
"7",
"6",
"1",
"0",
"2",
"3",
"0",
"1",
"3",
"2",
"6",
"7",
"5",
"4",
"7",
"6",
"4",
"5",
"0",
"1",
"3",
"2",
"1",
"0",
"2",
"3",
"7",
"6",
"4",
"5",
"6",
"7",
"5",
"4",
"2",
"3",
"1",
"0",
"3",
"2",
"0",
"1",
"5"
] |
[
"nonn",
"base",
"easy"
] | 28 | 0 | 3 |
[
"A000069",
"A001511",
"A001969",
"A003188",
"A003987",
"A006519",
"A010060",
"A253317",
"A261283",
"A269723",
"A355340"
] | null |
Peter Munn, Jun 29 2022
| 2024-05-29T07:04:26 |
oeisdata/seq/A355/A355340.seq
|
c9a845b0366e4eb374ce3ad5d3bb6447
|
A355341
|
G.f.: A(x) = Sum_{n=-oo..+oo} x^(n*(n+1)/2) * C(x)^n, where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).
|
[
"2",
"1",
"-2",
"1",
"-3",
"0",
"1",
"-4",
"2",
"0",
"1",
"-5",
"5",
"0",
"0",
"1",
"-6",
"9",
"-2",
"0",
"0",
"1",
"-7",
"14",
"-7",
"0",
"0",
"0",
"1",
"-8",
"20",
"-16",
"2",
"0",
"0",
"0",
"1",
"-9",
"27",
"-30",
"9",
"0",
"0",
"0",
"0",
"1",
"-10",
"35",
"-50",
"25",
"-2",
"0",
"0",
"0",
"0",
"1",
"-11",
"44",
"-77",
"55",
"-11",
"0",
"0",
"0",
"0",
"0",
"1",
"-12",
"54",
"-112",
"105",
"-36",
"2",
"0",
"0",
"0",
"0",
"0",
"1",
"-13",
"65",
"-156",
"182",
"-91",
"13",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"-14",
"77",
"-210",
"294",
"-196",
"49",
"-2",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"-15",
"90",
"-275",
"450",
"-378",
"140",
"-15",
"0",
"0",
"0",
"0",
"0",
"0",
"0"
] |
[
"sign"
] | 9 | 0 | 1 |
[
"A244422",
"A355341",
"A355342",
"A355343"
] | null |
Paul D. Hanna, Jul 21 2022
| 2022-07-24T03:57:27 |
oeisdata/seq/A355/A355341.seq
|
1e1884092d900a71d98c07aeb2963cab
|
A355342
|
G.f.: A(x) = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * C(x)^n, where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).
|
[
"0",
"1",
"-2",
"-1",
"3",
"0",
"1",
"-4",
"2",
"0",
"-1",
"5",
"-5",
"0",
"0",
"1",
"-6",
"9",
"-2",
"0",
"0",
"-1",
"7",
"-14",
"7",
"0",
"0",
"0",
"1",
"-8",
"20",
"-16",
"2",
"0",
"0",
"0",
"-1",
"9",
"-27",
"30",
"-9",
"0",
"0",
"0",
"0",
"1",
"-10",
"35",
"-50",
"25",
"-2",
"0",
"0",
"0",
"0",
"-1",
"11",
"-44",
"77",
"-55",
"11",
"0",
"0",
"0",
"0",
"0",
"1",
"-12",
"54",
"-112",
"105",
"-36",
"2",
"0",
"0",
"0",
"0",
"0",
"-1",
"13",
"-65",
"156",
"-182",
"91",
"-13",
"0",
"0",
"0",
"0",
"0",
"0",
"1",
"-14",
"77",
"-210",
"294",
"-196",
"49",
"-2",
"0",
"0",
"0",
"0",
"0",
"0",
"-1",
"15",
"-90",
"275",
"-450",
"378",
"-140",
"15",
"0",
"0",
"0",
"0",
"0",
"0",
"0"
] |
[
"sign"
] | 8 | 0 | 3 |
[
"A034807",
"A244422",
"A355341",
"A355342",
"A355343"
] | null |
Paul D. Hanna, Jul 22 2022
| 2022-07-24T03:57:32 |
oeisdata/seq/A355/A355342.seq
|
fec46d801b67b2448200baefb8f9bd78
|
A355343
|
G.f.: A(x,y) = Sum_{n=-oo..+oo} (x*y)^(n*(n+1)/2) * C(x)^n, where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108), as a triangle of coefficients T(n,k) of x^n*y^k in A(x,y), read by rows n >= 0.
|
[
"2",
"-1",
"2",
"-1",
"-1",
"0",
"-2",
"1",
"0",
"2",
"-5",
"3",
"0",
"-1",
"0",
"-14",
"9",
"0",
"5",
"0",
"0",
"-42",
"28",
"0",
"13",
"0",
"0",
"2",
"-132",
"90",
"0",
"39",
"0",
"0",
"-1",
"0",
"-429",
"297",
"0",
"123",
"0",
"0",
"11",
"0",
"0",
"-1430",
"1001",
"0",
"401",
"0",
"0",
"28",
"0",
"0",
"0",
"-4862",
"3432",
"0",
"1340",
"0",
"0",
"89",
"0",
"0",
"0",
"2",
"-16796",
"11934",
"0",
"4565",
"0",
"0",
"293",
"0",
"0",
"0",
"-1",
"0",
"-58786",
"41990",
"0",
"15795",
"0",
"0",
"987",
"0",
"0",
"0",
"19",
"0",
"0",
"-208012"
] |
[
"sign",
"tabl"
] | 10 | 0 | 1 |
[
"A000108",
"A355341",
"A355343",
"A355344"
] | null |
Paul D. Hanna, Jul 22 2022
| 2024-08-02T12:04:33 |
oeisdata/seq/A355/A355343.seq
|
312ccbda11113290976b9e7f590fb185
|
A355344
|
G.f.: A(x,y) = Sum_{n=-oo..+oo} (-1)^n * (x*y)^(n*(n+1)/2) * C(x)^n, where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108), as a triangle of coefficients T(n,k) of x^n*y^k in A(x,y), read by rows n >= 0.
|
[
"0",
"1",
"0",
"1",
"-3",
"0",
"2",
"-3",
"0",
"0",
"5",
"-7",
"0",
"5",
"0",
"14",
"-19",
"0",
"5",
"0",
"0",
"42",
"-56",
"0",
"15",
"0",
"0",
"0",
"132",
"-174",
"0",
"45",
"0",
"0",
"-7",
"0",
"429",
"-561",
"0",
"141",
"0",
"0",
"-7",
"0",
"0",
"1430",
"-1859",
"0",
"457",
"0",
"0",
"-28",
"0",
"0",
"0",
"4862",
"-6292",
"0",
"1520",
"0",
"0",
"-91",
"0",
"0",
"0",
"0",
"16796",
"-21658",
"0",
"5159",
"0",
"0",
"-301",
"0",
"0",
"0",
"9",
"0",
"58786",
"-75582",
"0",
"17797",
"0",
"0",
"-1015",
"0",
"0",
"0",
"9",
"0",
"0",
"208012"
] |
[
"sign",
"tabl"
] | 10 | 0 | 5 |
[
"A000108",
"A355342",
"A355343",
"A355344"
] | null |
Paul D. Hanna, Jul 22 2022
| 2024-08-02T12:04:25 |
oeisdata/seq/A355/A355344.seq
|
d43fcccddfa39da8e0f30e0cb542122f
|
A355345
|
G.f.: Sum_{n=-oo..+oo} x^(n*(n+1)/2) * C(x)^(2*n-1), where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).
|
[
"2",
"-2",
"-5",
"6",
"-7",
"14",
"-6",
"-9",
"27",
"-30",
"10",
"-11",
"44",
"-77",
"55",
"-10",
"-13",
"65",
"-156",
"182",
"-91",
"14",
"-15",
"90",
"-275",
"450",
"-378",
"140",
"-14",
"-17",
"119",
"-442",
"935",
"-1122",
"714",
"-204",
"18",
"-19",
"152",
"-665",
"1729",
"-2717",
"2508",
"-1254",
"285",
"-18",
"-21",
"189",
"-952",
"2940",
"-5733",
"7007",
"-5148",
"2079",
"-385",
"22",
"-23",
"230",
"-1311",
"4692",
"-10948",
"16744",
"-16445",
"9867",
"-3289",
"506"
] |
[
"sign"
] | 8 | 0 | 1 |
[
"A000108",
"A034807",
"A132460",
"A355341",
"A355342",
"A355345",
"A355346",
"A355347"
] | null |
Paul D. Hanna, Jul 25 2022
| 2022-07-27T10:30:52 |
oeisdata/seq/A355/A355345.seq
|
9eb1136f41326d92febba2812bbc366c
|
A355346
|
G.f.: A(x,y) = Sum_{n=-oo..+oo} (x*y)^(n*(n+1)/2) * C(x)^(2*n-1), where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).
|
[
"2",
"-4",
"2",
"-1",
"-4",
"0",
"-3",
"7",
"0",
"2",
"-8",
"5",
"0",
"-4",
"0",
"-23",
"14",
"0",
"23",
"0",
"0",
"-70",
"41",
"0",
"21",
"0",
"0",
"2",
"-222",
"127",
"0",
"90",
"0",
"0",
"-4",
"0",
"-726",
"409",
"0",
"297",
"0",
"0",
"47",
"0",
"0",
"-2431",
"1355",
"0",
"1001",
"0",
"0",
"45",
"0",
"0",
"0",
"-8294",
"4587",
"0",
"3431",
"0",
"0",
"284",
"0",
"0",
"0",
"2",
"-28730",
"15795",
"0",
"11927",
"0",
"0",
"1001",
"0",
"0",
"0",
"-4",
"0",
"-100776",
"55146",
"0",
"41955",
"0",
"0",
"3640",
"0",
"0",
"0",
"79",
"0",
"0",
"-357238",
"194752",
"0",
"149072",
"0",
"0",
"13260",
"0",
"0",
"0",
"77",
"0",
"0",
"0"
] |
[
"sign",
"tabl"
] | 7 | 0 | 1 |
[
"A000108",
"A355345",
"A355346"
] | null |
Paul D. Hanna, Jul 25 2022
| 2022-07-27T10:32:16 |
oeisdata/seq/A355/A355346.seq
|
e6ac935790db26db8b9097a7d828c18c
|
A355347
|
a(n) = binomial(3*n+3,n) + binomial(3*n+2,n-1) for n >= 0.
|
[
"1",
"7",
"44",
"275",
"1729",
"10948",
"69768",
"447051",
"2877875",
"18599295",
"120609840",
"784384692",
"5114119724",
"33417386200",
"218786861392",
"1434903854139",
"9425348845815",
"61997934676405",
"408323057257500",
"2692322893972635",
"17770644483690945",
"117406930477134480",
"776363580147660960"
] |
[
"nonn"
] | 7 | 0 | 2 |
[
"A001764",
"A355345",
"A355347"
] | null |
Paul D. Hanna, Jul 25 2022
| 2022-07-27T10:30:58 |
oeisdata/seq/A355/A355347.seq
|
69e87d1f61f08f5cd9120501be911015
|
A355348
|
G.f.: Sum_{n=-oo..+oo} x^(n*(n+1)/2) * C(x)^(3*n-3), where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108).
|
[
"2",
"-7",
"0",
"26",
"-42",
"63",
"-111",
"90",
"54",
"-273",
"451",
"-396",
"275",
"-561",
"1287",
"-1781",
"1365",
"-351",
"-871",
"2938",
"-5733",
"7008",
"-5172",
"2331",
"-1905",
"5835",
"-14688",
"24752",
"-27455",
"19278",
"-7684",
"-561",
"10251",
"-32317",
"69768",
"-104652",
"107407",
"-72960",
"31293",
"-10621",
"18069",
"-63783"
] |
[
"sign"
] | 13 | 0 | 1 |
[
"A000108",
"A355341",
"A355345",
"A355348"
] | null |
Paul D. Hanna, Jul 28 2022
| 2022-08-03T06:17:54 |
oeisdata/seq/A355/A355348.seq
|
96714aac95ff8dcf72cd32363fc52b94
|
A355349
|
G.f. A(x) satisfies: 2 = Sum_{n=-oo..+oo} (-x)^(n*(n-1)/2) * A(x)^(n^2).
|
[
"1",
"2",
"10",
"76",
"678",
"6608",
"68170",
"731638",
"8084692",
"91361298",
"1050937008",
"12264790410",
"144856757032",
"1728197200206",
"20796217437806",
"252117655811806",
"3076371017010508",
"37753163861001044",
"465657991700212170",
"5769586313420410060",
"71777257553636752194"
] |
[
"nonn"
] | 10 | 0 | 2 |
[
"A354248",
"A354662",
"A355349",
"A355871"
] | null |
Paul D. Hanna, Aug 02 2022
| 2024-01-31T06:28:51 |
oeisdata/seq/A355/A355349.seq
|
1929564e62896ce2a43655595a25bab5
|
A355350
|
G.f. A(x,y) satisfies: x*y = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x,y)^n, with coefficients T(n,k) of x^n*y^k in A(x,y) given as a triangle read by rows.
|
[
"1",
"0",
"1",
"0",
"3",
"1",
"0",
"9",
"6",
"1",
"0",
"22",
"27",
"10",
"1",
"0",
"51",
"98",
"66",
"15",
"1",
"0",
"108",
"315",
"340",
"135",
"21",
"1",
"0",
"221",
"918",
"1495",
"910",
"246",
"28",
"1",
"0",
"429",
"2492",
"5838",
"5070",
"2086",
"413",
"36",
"1",
"0",
"810",
"6372",
"20805",
"24543",
"14280",
"4284",
"652",
"45",
"1",
"0",
"1479",
"15525",
"68816",
"106535",
"83559",
"35168",
"8100",
"981",
"55",
"1",
"0",
"2640",
"36280",
"213945",
"423390",
"432930",
"243208",
"78282",
"14355",
"1420",
"66",
"1"
] |
[
"nonn",
"tabl"
] | 7 | 0 | 5 |
[
"A000041",
"A000716",
"A023005",
"A354645",
"A354650",
"A354658",
"A355350",
"A355351",
"A355352",
"A355353",
"A355354",
"A355355",
"A355356",
"A355357"
] | null |
Paul D. Hanna, Jun 29 2022
| 2022-06-30T10:39:21 |
oeisdata/seq/A355/A355350.seq
|
aa1923b2efc657f795b39b3992382f36
|
A355351
|
G.f. A(x) satisfies: x = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x)^n.
|
[
"1",
"1",
"4",
"16",
"60",
"231",
"920",
"3819",
"16365",
"71792",
"320219",
"1446517",
"6602975",
"30415725",
"141231704",
"660431602",
"3107519738",
"14701758926",
"69891556656",
"333700223891",
"1599475107712",
"7693580712200",
"37125486197570",
"179675330190428",
"871910824853956",
"4241603521253775"
] |
[
"nonn"
] | 8 | 0 | 3 |
[
"A355350",
"A355351",
"A355352",
"A355353",
"A355354",
"A355355",
"A355356",
"A355357"
] | null |
Paul D. Hanna, Jun 29 2022
| 2024-02-01T07:57:36 |
oeisdata/seq/A355/A355351.seq
|
a968819cccd5dc872f36d84c1cc78ca5
|
A355352
|
G.f. A(x) satisfies: 2*x = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x)^n.
|
[
"1",
"2",
"10",
"50",
"248",
"1294",
"7092",
"40426",
"236698",
"1412860",
"8561906",
"52546920",
"326011118",
"2041512624",
"12886608654",
"81908498582",
"523780469070",
"3367399778356",
"21752611767804",
"141118852010146",
"919035717462824",
"6006146649948722",
"39376700396145616",
"258907024677687808"
] |
[
"nonn"
] | 5 | 0 | 2 |
[
"A355350",
"A355351",
"A355352",
"A355353",
"A355354",
"A355355",
"A355356",
"A355357"
] | null |
Paul D. Hanna, Jun 29 2022
| 2022-06-30T10:39:45 |
oeisdata/seq/A355/A355352.seq
|
c76abe8ed64d3cceee7ba7fefd2c6ca3
|
A355353
|
G.f. A(x) satisfies: 3*x = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x)^n.
|
[
"1",
"3",
"18",
"108",
"660",
"4275",
"29106",
"205377",
"1485279",
"10943424",
"81866493",
"620316297",
"4751289063",
"36727782675",
"286153810542",
"2244799306134",
"17715992048886",
"140560480602810",
"1120518766292436",
"8970573523101477",
"72091628161825608",
"581375787259765554",
"4703286596619094686"
] |
[
"nonn"
] | 5 | 0 | 2 |
[
"A355350",
"A355351",
"A355352",
"A355353",
"A355354",
"A355355",
"A355356",
"A355357"
] | null |
Paul D. Hanna, Jun 29 2022
| 2022-06-30T10:39:56 |
oeisdata/seq/A355/A355353.seq
|
dc5be58797a3b7763eebc03a11644882
|
A355354
|
G.f. A(x) satisfies: 4*x = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x)^n.
|
[
"1",
"4",
"28",
"196",
"1416",
"10860",
"87392",
"727188",
"6196212",
"53783336",
"474011756",
"4231158016",
"38174676188",
"347566170384",
"3189295781780",
"29465038957708",
"273851282010308",
"2558703740102840",
"24019990008557160",
"226444571054525156",
"2142925363606256584",
"20349477565111498148"
] |
[
"nonn"
] | 5 | 0 | 2 |
[
"A355350",
"A355351",
"A355352",
"A355353",
"A355354",
"A355355",
"A355356",
"A355357"
] | null |
Paul D. Hanna, Jun 29 2022
| 2022-06-30T10:40:07 |
oeisdata/seq/A355/A355354.seq
|
6d03cbf64278166e1cf12d3ccaa98bbc
|
A355355
|
G.f. A(x) satisfies: 5*x = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x)^n.
|
[
"1",
"5",
"40",
"320",
"2660",
"23455",
"216540",
"2064055",
"20137945",
"200134600",
"2019406895",
"20635313325",
"213109960895",
"2220820915065",
"23323755734820",
"246616999661690",
"2623193780773530",
"28049464032800110",
"301340494687086960",
"3251017466141039095",
"35207152686408604400"
] |
[
"nonn"
] | 5 | 0 | 2 |
[
"A355350",
"A355351",
"A355352",
"A355353",
"A355354",
"A355355",
"A355356",
"A355357"
] | null |
Paul D. Hanna, Jun 29 2022
| 2022-06-30T10:40:16 |
oeisdata/seq/A355/A355355.seq
|
d840526a4574885c208d7917bc45663b
|
A355356
|
G.f. A(x) satisfies: x^2 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x)^n.
|
[
"1",
"0",
"1",
"3",
"10",
"28",
"79",
"216",
"603",
"1702",
"4933",
"14620",
"44287",
"136352",
"424858",
"1334162",
"4211572",
"13344072",
"42412667",
"135217722",
"432483522",
"1387929369",
"4469341807",
"14439523193",
"46795072968",
"152076428228",
"495460089510",
"1617787324674",
"5292984017236",
"17348743335252"
] |
[
"nonn"
] | 4 | 0 | 4 |
[
"A355350",
"A355351",
"A355352",
"A355353",
"A355354",
"A355355",
"A355356",
"A355357"
] | null |
Paul D. Hanna, Jun 29 2022
| 2022-06-30T10:40:25 |
oeisdata/seq/A355/A355356.seq
|
6b1357bf7e7935a62c9b20aadd695386
|
A355357
|
G.f. A(x) satisfies: x = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)) * A(x)^n.
|
[
"1",
"1",
"1",
"4",
"7",
"20",
"43",
"110",
"262",
"674",
"1684",
"4397",
"11320",
"29938",
"78641",
"210044",
"559724",
"1507563",
"4060585",
"11016027",
"29919220",
"81673846",
"223307300",
"612851316",
"1684816018",
"4645243490",
"12829177587",
"35513736868",
"98465916370",
"273531234027",
"760966444416"
] |
[
"nonn"
] | 11 | 0 | 4 |
[
"A355350",
"A355351",
"A355352",
"A355353",
"A355354",
"A355355",
"A355356",
"A355357",
"A357221",
"A357222",
"A357223",
"A357224",
"A357225",
"A357226",
"A359720"
] | null |
Paul D. Hanna, Jun 29 2022
| 2024-02-01T07:09:03 |
oeisdata/seq/A355/A355357.seq
|
ed93c884c7abb34bcb6dda9eac94c10d
|
A355358
|
Coefficients in the expansion of A(x) = 1 / Product_{n>=0} (1 - x^(13*n+1))*(1 - x^(13*n+3))*(1 - x^(13*n+4))*(1 - x^(13*n+9))*(1 - x^(13*n+10))*(1 - x^(13*n+12)).
|
[
"1",
"1",
"1",
"2",
"3",
"3",
"4",
"5",
"6",
"8",
"10",
"11",
"15",
"18",
"21",
"25",
"31",
"36",
"43",
"50",
"59",
"69",
"81",
"93",
"109",
"126",
"146",
"168",
"194",
"222",
"256",
"291",
"333",
"379",
"432",
"489",
"557",
"629",
"712",
"805",
"909",
"1021",
"1152",
"1293",
"1452",
"1627",
"1824",
"2037",
"2281",
"2544",
"2838",
"3162",
"3525",
"3916",
"4356"
] |
[
"nonn"
] | 12 | 0 | 4 |
[
"A214157",
"A341714",
"A355358",
"A355359"
] | null |
Paul D. Hanna, Jul 31 2022
| 2022-08-02T10:38:43 |
oeisdata/seq/A355/A355358.seq
|
8628ccab8cb838dcd5939a34ff7c4359
|
A355359
|
Coefficients in the expansion of B(x) = 1 / Product_{n>=0} (1 - x^(13*n+2))*(1 - x^(13*n+5))*(1 - x^(13*n+6))*(1 - x^(13*n+7))*(1 - x^(13*n+8))*(1 - x^(13*n+11)).
|
[
"1",
"0",
"1",
"0",
"1",
"1",
"2",
"2",
"3",
"2",
"4",
"4",
"6",
"6",
"8",
"9",
"11",
"12",
"16",
"17",
"22",
"24",
"29",
"32",
"39",
"43",
"53",
"57",
"69",
"75",
"90",
"99",
"117",
"129",
"150",
"166",
"193",
"213",
"246",
"273",
"312",
"346",
"394",
"436",
"496",
"549",
"621",
"687",
"774",
"855",
"962",
"1062",
"1192",
"1313",
"1470",
"1618",
"1807",
"1989",
"2214",
"2436"
] |
[
"nonn"
] | 12 | 0 | 7 |
[
"A214157",
"A341714",
"A355358",
"A355359"
] | null |
Paul D. Hanna, Aug 01 2022
| 2022-08-02T10:38:59 |
oeisdata/seq/A355/A355359.seq
|
badce0b172698b15848f638ce543a7f6
|
A355360
|
G.f. A(x,y) satisfies: x*y*A(x,y) = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x,y)^n, with coefficients T(n,k) of x^n*y^k in A(x,y) given as a triangle read by rows.
|
[
"1",
"0",
"1",
"0",
"3",
"2",
"0",
"9",
"12",
"5",
"0",
"22",
"54",
"46",
"14",
"0",
"51",
"196",
"282",
"175",
"42",
"0",
"108",
"630",
"1360",
"1365",
"666",
"132",
"0",
"221",
"1836",
"5635",
"8190",
"6321",
"2541",
"429",
"0",
"429",
"4984",
"20850",
"41405",
"45326",
"28448",
"9724",
"1430",
"0",
"810",
"12744",
"70737",
"184527",
"270060",
"237209",
"125532",
"37323",
"4862",
"0",
"1479",
"31050",
"223652",
"745745",
"1404102",
"1625932",
"1193116",
"546039",
"143650",
"16796"
] |
[
"nonn",
"tabl"
] | 7 | 0 | 5 |
[
"A000041",
"A000108",
"A000716",
"A023005",
"A355350",
"A355360",
"A355361",
"A355362",
"A355363",
"A355364",
"A355365"
] | null |
Paul D. Hanna, Jul 19 2022
| 2022-07-20T08:44:17 |
oeisdata/seq/A355/A355360.seq
|
6cf9ade0928b32edab1336c6fe8d5c54
|
A355361
|
G.f. A(x) satisfies: x*A(x) = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x)^n.
|
[
"1",
"1",
"5",
"26",
"136",
"746",
"4261",
"25173",
"152596",
"943804",
"5931561",
"37768700",
"243124702",
"1579577423",
"10344340396",
"68212177180",
"452531832109",
"3018280278965",
"20227324602249",
"136135295125566",
"919757424512780",
"6235752585125348",
"42411283395662960",
"289289349007740037"
] |
[
"nonn"
] | 14 | 0 | 3 |
[
"A355360",
"A355361",
"A355362",
"A355363",
"A355364",
"A355365"
] | null |
Paul D. Hanna, Jul 19 2022
| 2024-01-19T08:56:43 |
oeisdata/seq/A355/A355361.seq
|
72f839ce2a167675a5922f32639903b7
|
A355362
|
G.f. A(x) satisfies: 2*x*A(x) = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x)^n.
|
[
"1",
"2",
"14",
"106",
"852",
"7286",
"65216",
"603714",
"5731930",
"55506348",
"546091942",
"5443033448",
"54845812094",
"557774491672",
"5717718435034",
"59017814463718",
"612873311614338",
"6398538141213916",
"67121038262747380",
"707114126290890810",
"7478082640450505012",
"79360375914717108922"
] |
[
"nonn"
] | 9 | 0 | 2 |
[
"A355360",
"A355361",
"A355362",
"A355363",
"A355364",
"A355365"
] | null |
Paul D. Hanna, Jul 19 2022
| 2025-07-03T12:50:37 |
oeisdata/seq/A355/A355362.seq
|
20d172364031aba6a42cbd6bcc80d6b9
|
A355363
|
G.f. A(x) satisfies: 3*x*A(x) = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x)^n.
|
[
"1",
"3",
"27",
"270",
"2928",
"33912",
"411345",
"5159337",
"66364326",
"870637086",
"11604385575",
"156697653654",
"2139109221960",
"29472597414681",
"409312118499336",
"5723853297702444",
"80528723782556475",
"1139033786793330429",
"16187921479930951917",
"231046413762053945958"
] |
[
"nonn"
] | 8 | 0 | 2 |
[
"A355360",
"A355361",
"A355362",
"A355363",
"A355364",
"A355365"
] | null |
Paul D. Hanna, Jul 19 2022
| 2025-07-03T12:53:19 |
oeisdata/seq/A355/A355363.seq
|
7081af2baf39317f43d39d75ee6dca0d
|
A355364
|
G.f. A(x) satisfies: x^2*A(x) = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * A(x)^n.
|
[
"1",
"0",
"1",
"3",
"11",
"34",
"110",
"350",
"1147",
"3800",
"12836",
"43929",
"152285",
"533205",
"1883187",
"6698612",
"23974179",
"86258459",
"311811314",
"1131863444",
"4124127216",
"15078422405",
"55301519095",
"203405409935",
"750122683729",
"2773048061073",
"10274442343829",
"38147288401915"
] |
[
"nonn"
] | 8 | 0 | 4 |
[
"A355360",
"A355361",
"A355362",
"A355363",
"A355364",
"A355365"
] | null |
Paul D. Hanna, Jul 19 2022
| 2025-07-03T12:55:48 |
oeisdata/seq/A355/A355364.seq
|
767a0ec269d426f255ea6359910f7098
|
A355365
|
Central terms of A355360; a(n) = A355360(2*n,n).
|
[
"1",
"3",
"54",
"1360",
"41405",
"1404102",
"51126740",
"1957600876",
"77812428681",
"3183756066040",
"133302637049516",
"5687179333193904",
"246453229359401883",
"10821674290217357756",
"480561612716912592360",
"21549547977144582750304",
"974600584933918611940825",
"44409401763058366474029057"
] |
[
"nonn"
] | 8 | 0 | 2 |
[
"A355360",
"A355361",
"A355362",
"A355363",
"A355364",
"A355365"
] | null |
Paul D. Hanna, Jul 19 2022
| 2023-03-19T05:47:37 |
oeisdata/seq/A355/A355365.seq
|
af24c23ad9221a22eb63a519c815b3d7
|
A355366
|
Maximal GCD of five positive integers with sum n.
|
[
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"3",
"2",
"1",
"3",
"1",
"4",
"3",
"2",
"1",
"4",
"5",
"2",
"3",
"4",
"1",
"6",
"1",
"4",
"3",
"2",
"7",
"6",
"1",
"2",
"3",
"8",
"1",
"7",
"1",
"4",
"9",
"2",
"1",
"8",
"7",
"10",
"3",
"4",
"1",
"9",
"11",
"8",
"3",
"2",
"1",
"12",
"1",
"2",
"9",
"8",
"13",
"11",
"1",
"4",
"3",
"14",
"1",
"12",
"1",
"2",
"15",
"4",
"11",
"13",
"1",
"16",
"9",
"2",
"1",
"14",
"17",
"2",
"3",
"11",
"1"
] |
[
"nonn"
] | 15 | 5 | 6 |
[
"A008382",
"A032742",
"A129650",
"A354598",
"A354599",
"A354601",
"A355249",
"A355319",
"A355366",
"A355368",
"A355402"
] | null |
Wesley Ivan Hurt, Jun 29 2022
| 2022-09-21T11:28:02 |
oeisdata/seq/A355/A355366.seq
|
1d21918a4bc1e1a2e2329e16b38f7db4
|
A355367
|
Maximal LCM of six positive integers with sum n.
|
[
"1",
"2",
"3",
"6",
"6",
"12",
"15",
"30",
"30",
"60",
"60",
"84",
"105",
"210",
"210",
"420",
"420",
"420",
"420",
"840",
"840",
"1260",
"1260",
"2310",
"2310",
"4620",
"4620",
"5460",
"5460",
"9240",
"9240",
"13860",
"13860",
"16380",
"16380",
"30030",
"27720",
"60060",
"32760",
"40040",
"60060",
"120120",
"60060",
"180180",
"120120",
"157080",
"120120",
"360360"
] |
[
"nonn"
] | 15 | 6 | 2 |
[
"A008881",
"A129647",
"A129648",
"A129649",
"A129650",
"A355367",
"A355403"
] | null |
Wesley Ivan Hurt, Jun 29 2022
| 2023-06-23T13:22:25 |
oeisdata/seq/A355/A355367.seq
|
1bf729d90b713539a419d035724b8444
|
A355368
|
Maximal GCD of six positive integers with sum n.
|
[
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"3",
"1",
"2",
"3",
"2",
"1",
"4",
"1",
"2",
"3",
"4",
"1",
"5",
"1",
"4",
"3",
"2",
"5",
"6",
"1",
"2",
"3",
"5",
"1",
"7",
"1",
"4",
"5",
"2",
"1",
"8",
"7",
"5",
"3",
"4",
"1",
"9",
"5",
"8",
"3",
"2",
"1",
"10",
"1",
"2",
"9",
"8",
"5",
"11",
"1",
"4",
"3",
"10",
"1",
"12",
"1",
"2",
"5",
"4",
"11",
"13",
"1",
"10",
"9",
"2",
"1",
"14",
"5",
"2",
"3",
"11",
"1",
"15",
"13",
"4",
"3",
"2"
] |
[
"nonn"
] | 12 | 6 | 7 |
[
"A008881",
"A032742",
"A354598",
"A354599",
"A354601",
"A355249",
"A355319",
"A355366",
"A355367",
"A355368",
"A355402"
] | null |
Wesley Ivan Hurt, Jun 29 2022
| 2022-09-21T07:42:00 |
oeisdata/seq/A355/A355368.seq
|
38dedd7c06549496916fdb00cacf5589
|
A355369
|
a(n) is the least prime p such that the sum of the product of the n consecutive primes starting with p and the decimal digits of those primes is prime.
|
[
"11",
"2",
"167",
"2",
"19",
"5",
"911",
"2",
"61",
"59",
"919",
"29",
"337",
"919",
"983",
"29",
"541",
"311",
"1721",
"359",
"757",
"419",
"877",
"61",
"59",
"151",
"16943",
"1637",
"1439",
"71",
"3739",
"557",
"443",
"1303",
"353",
"569",
"2381",
"97",
"2389",
"5519",
"617",
"1381",
"89",
"7",
"1103",
"733",
"409",
"521",
"499",
"283",
"911",
"709",
"5113",
"179",
"9157",
"3533",
"971",
"47",
"3191",
"3917"
] |
[
"nonn",
"base"
] | 8 | 1 | 1 | null | null |
J. M. Bergot and Robert Israel, Jun 30 2022
| 2022-06-30T14:45:12 |
oeisdata/seq/A355/A355369.seq
|
e80b86ab881e7834c8f0124367ed3172
|
A355370
|
Irregular triangle read by rows in which row n lists the numbers that divide the sum of the digits of their n-th powers.
|
[
"1",
"1",
"2",
"3",
"4",
"5",
"6",
"7",
"8",
"9",
"1",
"2",
"3",
"9",
"1",
"2",
"3",
"8",
"9",
"17",
"18",
"26",
"27",
"1",
"3",
"6",
"7",
"9",
"22",
"25",
"28",
"36",
"1",
"3",
"9",
"28",
"35",
"36",
"46",
"1",
"2",
"3",
"7",
"9",
"18",
"23",
"45",
"54",
"64",
"1",
"3",
"6",
"9",
"12",
"15",
"18",
"27",
"31",
"34",
"43",
"53",
"58",
"68",
"1",
"3",
"5",
"6",
"9",
"15",
"27",
"46",
"54",
"63"
] |
[
"tabf",
"nonn",
"base"
] | 29 | 0 | 3 |
[
"A046000",
"A152147",
"A309017",
"A355370",
"A355563"
] | null |
Mohammed Yaseen, Jun 30 2022
| 2022-07-15T21:48:56 |
oeisdata/seq/A355/A355370.seq
|
56850e00f3b394f9449ca6d895435f4b
|
A355371
|
Intersection of A000330 and A086849.
|
[
"5",
"91",
"506",
"650",
"11440"
] |
[
"nonn",
"more"
] | 11 | 1 | 1 |
[
"A000330",
"A086849",
"A355371"
] | null |
Ivan N. Ianakiev, Jun 30 2022
| 2022-07-09T15:36:29 |
oeisdata/seq/A355/A355371.seq
|
bb88b0ed2c5172bedff2b70d90f99de5
|
A355372
|
Expansion of the e.g.f. log((1 - x) / (1 - 2*x)) / (1 - x)^3.
|
[
"0",
"1",
"9",
"77",
"714",
"7374",
"85272",
"1102968",
"15908400",
"254866320",
"4516084800",
"88102382400",
"1883199024000",
"43885950595200",
"1109416142822400",
"30273281955302400",
"887493144729139200",
"27827941161784780800",
"929449073791558656000",
"32943696020637889536000",
"1234946945823695419392000"
] |
[
"nonn"
] | 8 | 0 | 3 |
[
"A000292",
"A062139",
"A355171",
"A355372"
] | null |
Mélika Tebni, Jun 30 2022
| 2022-07-01T00:05:54 |
oeisdata/seq/A355/A355372.seq
|
4b19ea5464294388aa8ec3f1bda43ae6
|
A355373
|
a(n) = Sum_{k=0..n} k! * (-1)^k * n^(n-k) * Stirling2(n,k).
|
[
"1",
"-1",
"0",
"3",
"40",
"455",
"2016",
"-177373",
"-11564160",
"-497664081",
"-12796467200",
"536297904659",
"132025634657280",
"14907422733429239",
"1181852660381503488",
"34684559693802943875",
"-11771644802057621110784",
"-3553614228958108389522721",
"-656899368126170250221715456"
] |
[
"sign"
] | 14 | 0 | 4 |
[
"A212846",
"A213127",
"A213128",
"A213129",
"A213130",
"A213131",
"A213132",
"A213133",
"A318183",
"A352074",
"A355373"
] | null |
Seiichi Manyama, Jun 30 2022
| 2022-06-30T08:37:12 |
oeisdata/seq/A355/A355373.seq
|
91e0ab65a0427c27ed4d214613fc9a7e
|
A355374
|
a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared such that the number of proper divisors of a(n) equals the number of 1-bits in the binary expansion of a(n-1).
|
[
"1",
"2",
"3",
"4",
"5",
"9",
"25",
"6",
"49",
"8",
"7",
"10",
"121",
"12",
"169",
"16",
"11",
"14",
"15",
"81",
"21",
"22",
"26",
"27",
"625",
"18",
"289",
"33",
"361",
"20",
"529",
"34",
"841",
"28",
"35",
"38",
"39",
"2401",
"32",
"13",
"46",
"14641",
"24",
"961",
"44",
"51",
"28561",
"48",
"1369",
"64",
"17",
"1681",
"45",
"83521",
"729",
"15625",
"30",
"130321",
"1024",
"19",
"55",
"50",
"57",
"279841",
"117649"
] |
[
"nonn",
"base",
"look"
] | 14 | 1 | 2 |
[
"A000120",
"A005179",
"A027751",
"A032741",
"A355374"
] | null |
Scott R. Shannon, Jun 30 2022
| 2022-07-03T09:11:28 |
oeisdata/seq/A355/A355374.seq
|
ebd2e2c486200b305c482e6839a23f08
|
A355375
|
a(n) = Sum_{k=0..n} (-k)^(n-k) * Stirling2(n,k).
|
[
"1",
"1",
"0",
"-4",
"10",
"67",
"-969",
"3341",
"86976",
"-1988704",
"14144108",
"405611857",
"-17544321563",
"287677263837",
"3595470378748",
"-421298868094940",
"14476946230894114",
"-112253861285434961",
"-18711849695261432065",
"1354595712379990848137",
"-44436925726445545236496"
] |
[
"sign"
] | 15 | 0 | 4 |
[
"A229233",
"A232549",
"A318183",
"A355375",
"A355376"
] | null |
Seiichi Manyama, Jun 30 2022
| 2022-06-30T10:27:29 |
oeisdata/seq/A355/A355375.seq
|
987e1c3997f3309aaed463fd5c74fdcd
|
A355376
|
a(n) = Sum_{k=0..n} k! * (-k)^(n-k) * Stirling2(n,k).
|
[
"1",
"1",
"1",
"-5",
"-29",
"271",
"3091",
"-61025",
"-744029",
"34875871",
"211095331",
"-37415273345",
"300267009571",
"61080483836191",
"-2133136977892829",
"-119576844586022465",
"11752559492568148771",
"94348367247493654111",
"-68793303669649907424989",
"2764486881197709482575615"
] |
[
"sign"
] | 14 | 0 | 4 |
[
"A229234",
"A355373",
"A355375",
"A355376"
] | null |
Seiichi Manyama, Jun 30 2022
| 2022-06-30T10:15:42 |
oeisdata/seq/A355/A355376.seq
|
b6460e91562e5a57521e27c57ab73f78
|
A355377
|
Numbers k such that the concatenation of digits included in the sum and product of the digits of the number k is an anagram of the number k, and digits of the number are sorted in nondecreasing order.
|
[
"119",
"1236",
"11359",
"11449",
"122669",
"2334699",
"13346899"
] |
[
"nonn",
"base",
"fini",
"full"
] | 41 | 1 | 1 |
[
"A062237",
"A355377"
] | null |
Ilya Orlov, Jun 30 2022
| 2022-07-01T22:08:54 |
oeisdata/seq/A355/A355377.seq
|
3837be57e6c7fa2fed29a358416fd229
|
A355378
|
Expansion of e.g.f. exp(exp(3*x) - exp(x)).
|
[
"1",
"2",
"12",
"82",
"688",
"6754",
"75096",
"928386",
"12591392",
"185384130",
"2938319144",
"49799613538",
"897495547184",
"17118975292514",
"344206910941624",
"7270287035936706",
"160826794265399360",
"3716047107259486082",
"89472755268582494792",
"2240097688067896960674",
"58207872357772581544272"
] |
[
"nonn"
] | 18 | 0 | 2 |
[
"A143405",
"A355291",
"A355378",
"A355379",
"A355381"
] | null |
Vaclav Kotesovec, Jun 30 2022
| 2022-07-10T07:12:52 |
oeisdata/seq/A355/A355378.seq
|
a967473db8c529a952d25c763bee2f29
|
A355379
|
Expansion of e.g.f. exp(exp(3*x) + exp(x) - 2).
|
[
"1",
"4",
"26",
"212",
"2046",
"22588",
"278942",
"3792916",
"56128254",
"895795692",
"15307847614",
"278435732484",
"5364073445278",
"108994074306268",
"2327475127169182",
"52069279762495220",
"1217024509006768574",
"29647115491635327180",
"751085909757123127294",
"19750410883486281805028"
] |
[
"nonn"
] | 17 | 0 | 2 |
[
"A143405",
"A355291",
"A355378",
"A355379"
] | null |
Vaclav Kotesovec, Jun 30 2022
| 2022-07-10T07:13:59 |
oeisdata/seq/A355/A355379.seq
|
04d582b18b8a5b670770edc5fd90b677
|
A355380
|
Expansion of e.g.f. exp(exp(3*x) + exp(2*x) - 2).
|
[
"1",
"5",
"38",
"355",
"3879",
"48050",
"661163",
"9961745",
"162598044",
"2851150665",
"53350521523",
"1059447004560",
"22224898346989",
"490589320542305",
"11356591577861398",
"274886065370874775",
"6939205217774546339",
"182273695066097752170",
"4971724931587003394863",
"140559648864263508395965"
] |
[
"nonn"
] | 15 | 0 | 2 |
[
"A143405",
"A355291",
"A355380",
"A355381"
] | null |
Vaclav Kotesovec, Jun 30 2022
| 2022-07-03T04:45:25 |
oeisdata/seq/A355/A355380.seq
|
a0c52afecb7db86c7a4c136842a72c1e
|
A355381
|
Expansion of e.g.f. exp(exp(3*x) - exp(2*x)).
|
[
"1",
"1",
"6",
"35",
"247",
"2102",
"20547",
"224541",
"2707292",
"35638329",
"507464939",
"7757439428",
"126538995293",
"2191454313661",
"40120212534838",
"773554002955047",
"15656660861190371",
"331700076893737054",
"7337160433117899959",
"169068422994937678185",
"4050093664805130165348"
] |
[
"nonn"
] | 22 | 0 | 3 |
[
"A143405",
"A194006",
"A355291",
"A355378",
"A355380",
"A355381"
] | null |
Vaclav Kotesovec, Jun 30 2022
| 2022-07-11T11:28:08 |
oeisdata/seq/A355/A355381.seq
|
72bc2052272fc913c16c2069c1bb42f6
|
A355382
|
Number of divisors d of n such that bigomega(d) = omega(n).
|
[
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"1",
"1",
"1",
"3",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"2",
"2",
"1",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"2",
"1",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"2",
"2",
"1",
"1",
"1",
"2",
"1",
"1",
"1",
"3",
"1",
"1",
"1"
] |
[
"nonn"
] | 10 | 1 | 12 |
[
"A000005",
"A000712",
"A001221",
"A001222",
"A022811",
"A056239",
"A070175",
"A071625",
"A118914",
"A133494",
"A181591",
"A181819",
"A182850",
"A303555",
"A323014",
"A323022",
"A323023",
"A339006",
"A355382",
"A355383",
"A355384",
"A355385",
"A355386",
"A355388"
] | null |
Gus Wiseman, Jul 02 2022
| 2022-07-03T23:56:23 |
oeisdata/seq/A355/A355382.seq
|
0b5651c67782378135d43f7ccdab16e0
|
A355383
|
Number of pairs (y, v), where y is a partition of n and v is a sub-multiset of y whose cardinality equals the number of distinct parts in y.
|
[
"1",
"1",
"2",
"3",
"6",
"10",
"16",
"26",
"42",
"64",
"100",
"150",
"224",
"330",
"482",
"697",
"999",
"1418",
"1996",
"2794",
"3879",
"5355",
"7343",
"10018",
"13583",
"18338",
"24618",
"32917",
"43790",
"58043",
"76591",
"100716",
"131906",
"172194",
"223966",
"290423",
"375318",
"483668",
"621368",
"796138",
"1017146"
] |
[
"nonn"
] | 9 | 0 | 3 |
[
"A000009",
"A001970",
"A022811",
"A032020",
"A063834",
"A070933",
"A072706",
"A181591",
"A181819",
"A316245",
"A317715",
"A318683",
"A318684",
"A319794",
"A319910",
"A323433",
"A323583",
"A336131",
"A336136",
"A339006",
"A355382",
"A355383",
"A355384",
"A355385",
"A355388"
] | null |
Gus Wiseman, Jul 02 2022
| 2022-07-03T23:56:28 |
oeisdata/seq/A355/A355383.seq
|
607ffb43ba0a99723cd2d0ff8911c68e
|
A355384
|
Number of pairs (y, v) where y is a composition of n and v is a (not necessarily contiguous) subsequence of y whose length equals the number of distinct parts in y.
|
[
"1",
"1",
"2",
"4",
"12",
"30",
"66",
"164",
"419",
"1049",
"2625",
"6372",
"15451",
"37335",
"89855",
"216523",
"518714",
"1235897",
"2930050",
"6911149",
"16217817",
"37914515",
"88304358",
"204971388",
"474172899",
"1093547574",
"2513959446",
"5761735383",
"13165908506",
"29998936859",
"68164839887",
"154478212575"
] |
[
"nonn"
] | 14 | 0 | 3 |
[
"A000009",
"A000244",
"A001970",
"A022811",
"A032020",
"A063834",
"A070933",
"A072706",
"A133494",
"A323583",
"A336139",
"A339006",
"A355383",
"A355384",
"A355385",
"A355388"
] | null |
Gus Wiseman, Jul 01 2022
| 2025-05-09T01:45:34 |
oeisdata/seq/A355/A355384.seq
|
2cda2e65c4e00474937049244ce3ed62
|
A355385
|
Number of pairs (y, v) of integer partitions of n where the length of v equals the number of distinct parts in y.
|
[
"1",
"1",
"2",
"3",
"7",
"12",
"25",
"43",
"81",
"141",
"243",
"409",
"699",
"1132",
"1844",
"2995",
"4744",
"7408",
"11655",
"17839",
"27509",
"41546",
"62879",
"93537",
"139974",
"205547",
"302714",
"440097",
"640968",
"921774",
"1327538",
"1891548",
"2696635",
"3809860",
"5380257",
"7540778",
"10561566",
"14687109",
"20408170",
"28183998",
"38882009"
] |
[
"nonn"
] | 10 | 0 | 3 |
[
"A000009",
"A001970",
"A008284",
"A022811",
"A032020",
"A063834",
"A070933",
"A072706",
"A116608",
"A279787",
"A319910",
"A323583",
"A336135",
"A339006",
"A355383",
"A355384",
"A355385",
"A355388"
] | null |
Gus Wiseman, Jul 02 2022
| 2022-12-31T20:30:03 |
oeisdata/seq/A355/A355385.seq
|
f4e025472d76c59e0c0ce176a07921c8
|
A355386
|
Position of first appearance of n in A355382, where A355382(m) = number of divisors d of m such that bigomega(d) = omega(m); or a(n) = -1 if n does not appear in A355382.
|
[
"1",
"12",
"36",
"120",
"180",
"360",
"840",
"1260",
"5400",
"27000",
"2520",
"5040",
"6300",
"7560",
"15120",
"12600",
"25200"
] |
[
"nonn",
"more"
] | 13 | 1 | 2 |
[
"A000005",
"A000712",
"A001221",
"A001222",
"A022811",
"A056239",
"A070175",
"A071625",
"A181591",
"A181819",
"A303555",
"A319910",
"A339006",
"A355382",
"A355383",
"A355384",
"A355386"
] | null |
Gus Wiseman, Jul 02 2022
| 2022-07-07T23:30:11 |
oeisdata/seq/A355/A355386.seq
|
cd7cb117657cd18a9259b06439758ad7
|
A355387
|
Number of ways to choose a distinct subsequence of an integer composition of n.
|
[
"1",
"2",
"5",
"14",
"37",
"98",
"259",
"682",
"1791",
"4697",
"12303",
"32196",
"84199",
"220087",
"575067",
"1502176",
"3923117",
"10244069",
"26746171",
"69825070",
"182276806",
"475804961",
"1241965456",
"3241732629",
"8461261457",
"22084402087",
"57640875725",
"150442742575",
"392652788250",
"1024810764496"
] |
[
"nonn"
] | 19 | 0 | 2 |
[
"A000302",
"A000712",
"A011782",
"A022811",
"A025192",
"A032005",
"A032020",
"A063834",
"A070933",
"A075900",
"A133494",
"A181591",
"A236002",
"A304961",
"A307068",
"A323583",
"A331330",
"A336127",
"A336128",
"A336130",
"A336139",
"A339006",
"A355382",
"A355383",
"A355384",
"A355387",
"A355388"
] | null |
Gus Wiseman, Jul 04 2022
| 2025-05-06T10:04:23 |
oeisdata/seq/A355/A355387.seq
|
0f2cc6531d9872966fc75c7e8c00c3a1
|
A355388
|
Number of composable pairs (y, v) of integer compositions of n, where a composition is regarded as an arrow from the number of parts to the number of distinct parts.
|
[
"1",
"1",
"2",
"6",
"18",
"58",
"174",
"536",
"1656",
"4947",
"14800",
"43157",
"126572",
"364070",
"1039926",
"2938898",
"8223400",
"22846370",
"62930113",
"172177400",
"467002792",
"1259736804",
"3371190792",
"8973530491",
"23728305128",
"62421018163",
"163255839779",
"424842462529",
"1100006243934",
"2834558927244",
"7270915592897"
] |
[
"nonn"
] | 15 | 0 | 3 |
[
"A000009",
"A001970",
"A022811",
"A032020",
"A063834",
"A070933",
"A133494",
"A316245",
"A319910",
"A323583",
"A336139",
"A355382",
"A355383",
"A355384",
"A355385",
"A355388"
] | null |
Gus Wiseman, Jul 02 2022
| 2023-01-01T20:19:59 |
oeisdata/seq/A355/A355388.seq
|
cddd8ccf41a26b597be32ae671016559
|
A355389
|
Number of unordered pairs of distinct integer partitions of n.
|
[
"0",
"0",
"1",
"3",
"10",
"21",
"55",
"105",
"231",
"435",
"861",
"1540",
"2926",
"5050",
"9045",
"15400",
"26565",
"43956",
"73920",
"119805",
"196251",
"313236",
"501501",
"786885",
"1239525",
"1915903",
"2965830",
"4528545",
"6909903",
"10417330",
"15699606",
"23403061",
"34848726",
"51435153",
"75761895",
"110744403",
"161577276"
] |
[
"nonn"
] | 13 | 0 | 4 |
[
"A000009",
"A000041",
"A001255",
"A001970",
"A006516",
"A022811",
"A063834",
"A070933",
"A086737",
"A316245",
"A317715",
"A319794",
"A319910",
"A323433",
"A339006",
"A355385",
"A355389",
"A355390"
] | null |
Gus Wiseman, Jul 04 2022
| 2024-02-07T21:07:47 |
oeisdata/seq/A355/A355389.seq
|
26f72b00baeded525dd93b80d884a18f
|
A355390
|
Number of ordered pairs of distinct integer partitions of n.
|
[
"0",
"0",
"2",
"6",
"20",
"42",
"110",
"210",
"462",
"870",
"1722",
"3080",
"5852",
"10100",
"18090",
"30800",
"53130",
"87912",
"147840",
"239610",
"392502",
"626472",
"1003002",
"1573770",
"2479050",
"3831806",
"5931660",
"9057090",
"13819806",
"20834660",
"31399212",
"46806122",
"69697452",
"102870306",
"151523790",
"221488806"
] |
[
"nonn"
] | 10 | 0 | 3 |
[
"A000009",
"A000041",
"A001255",
"A001970",
"A006516",
"A020522",
"A022811",
"A063834",
"A070933",
"A086737",
"A316245",
"A317715",
"A319910",
"A323433",
"A323583",
"A339006",
"A355385",
"A355389",
"A355390"
] | null |
Gus Wiseman, Jul 04 2022
| 2022-07-05T06:47:25 |
oeisdata/seq/A355/A355390.seq
|
d0baa9d0981dac9d55eb713e950d3f7d
|
A355391
|
Position of first appearance of n in A181591 = binomial(bigomega(n), omega(n)).
|
[
"1",
"4",
"8",
"16",
"32",
"24",
"128",
"256",
"512",
"48",
"2048",
"4096",
"8192",
"16384",
"96",
"65536",
"131072",
"262144",
"524288",
"240",
"192",
"4194304",
"8388608",
"16777216",
"33554432",
"67108864",
"134217728",
"384",
"536870912",
"1073741824",
"2147483648",
"4294967296",
"8589934592",
"17179869184",
"480",
"768",
"137438953472"
] |
[
"nonn"
] | 21 | 1 | 2 |
[
"A000005",
"A001221",
"A001222",
"A006987",
"A022811",
"A056239",
"A070175",
"A071625",
"A118914",
"A181819",
"A185024",
"A303555",
"A323014",
"A323023",
"A339006",
"A355383",
"A355384",
"A355386",
"A355391",
"A355392"
] | null |
Gus Wiseman, Jul 04 2022
| 2022-07-10T13:23:42 |
oeisdata/seq/A355/A355391.seq
|
5d484b66773566cae113b4bf3cc9f400
|
A355392
|
Sorted positions of first appearances in A181591 = binomial(bigomega(n), omega(n)).
|
[
"1",
"4",
"8",
"16",
"24",
"32",
"48",
"96",
"128",
"192",
"240",
"256",
"384",
"480",
"512",
"768",
"960",
"1536",
"1920",
"2048",
"3072",
"3360",
"3840",
"4096",
"6144",
"6720",
"7680",
"8192",
"12288",
"13440",
"15360",
"16384",
"24576",
"26880",
"30720",
"49152",
"53760",
"61440",
"65536",
"73920",
"107520",
"122880",
"131072",
"147840",
"196608"
] |
[
"nonn"
] | 13 | 1 | 2 |
[
"A000005",
"A000712",
"A001221",
"A001222",
"A022811",
"A056239",
"A070175",
"A071625",
"A118914",
"A181819",
"A303555",
"A323023",
"A355384",
"A355386",
"A355391",
"A355392"
] | null |
Gus Wiseman, Jul 04 2022
| 2022-07-10T13:22:11 |
oeisdata/seq/A355/A355392.seq
|
e120054dec8645c49e7a48d89f2a1e91
|
A355393
|
Number of integer partitions of n such that, for all parts x of multiplicity 1, either x - 1 or x + 1 is also a part.
|
[
"1",
"0",
"1",
"2",
"3",
"4",
"6",
"7",
"10",
"14",
"17",
"23",
"32",
"39",
"51",
"67",
"83",
"105",
"134",
"165",
"206",
"256",
"312",
"385",
"475",
"573",
"697",
"849",
"1021",
"1231",
"1483",
"1771",
"2121",
"2534",
"3007",
"3575",
"4245",
"5008",
"5914",
"6979",
"8198",
"9626",
"11292",
"13201",
"15430",
"18010",
"20960",
"24389",
"28346",
"32855",
"38066"
] |
[
"nonn"
] | 6 | 0 | 4 |
[
"A000009",
"A000041",
"A000837",
"A007690",
"A073491",
"A183558",
"A289509",
"A325160",
"A328171",
"A328172",
"A328187",
"A328220",
"A355393",
"A355394",
"A356233",
"A356235",
"A356236",
"A356237",
"A356606",
"A356607"
] | null |
Gus Wiseman, Aug 26 2022
| 2022-08-26T16:52:36 |
oeisdata/seq/A355/A355393.seq
|
e409146df98f08a847a3489ac63cf7ef
|
A355394
|
Number of integer partitions of n such that, for all parts x, x - 1 or x + 1 is also a part.
|
[
"1",
"0",
"0",
"1",
"1",
"3",
"3",
"6",
"6",
"10",
"11",
"16",
"18",
"25",
"30",
"38",
"47",
"59",
"74",
"90",
"112",
"136",
"171",
"203",
"253",
"299",
"372",
"438",
"536",
"631",
"767",
"900",
"1085",
"1271",
"1521",
"1774",
"2112",
"2463",
"2910",
"3389",
"3977",
"4627",
"5408",
"6276",
"7304",
"8459",
"9808",
"11338",
"13099",
"15112",
"17404",
"20044",
"23018",
"26450",
"30299",
"34746",
"39711",
"45452",
"51832"
] |
[
"nonn"
] | 24 | 0 | 6 |
[
"A000009",
"A000041",
"A000837",
"A007690",
"A066312",
"A073491",
"A077855",
"A183558",
"A289509",
"A328171",
"A328172",
"A328187",
"A328221",
"A355393",
"A355394",
"A356233",
"A356235",
"A356236",
"A356237",
"A356606",
"A356607",
"A356734",
"A356736"
] | null |
Gus Wiseman, Aug 26 2022
| 2024-02-17T14:08:02 |
oeisdata/seq/A355/A355394.seq
|
d38a38ad25ff1846dfe1239b08641ace
|
A355395
|
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^(j*(n-j)) * binomial(n,j).
|
[
"1",
"1",
"2",
"1",
"2",
"2",
"1",
"2",
"4",
"2",
"1",
"2",
"6",
"8",
"2",
"1",
"2",
"8",
"26",
"16",
"2",
"1",
"2",
"10",
"56",
"162",
"32",
"2",
"1",
"2",
"12",
"98",
"704",
"1442",
"64",
"2",
"1",
"2",
"14",
"152",
"2050",
"15392",
"18306",
"128",
"2",
"1",
"2",
"16",
"218",
"4752",
"84482",
"593408",
"330626",
"256",
"2",
"1",
"2",
"18",
"296",
"9506",
"318752",
"7221250",
"39691136",
"8488962",
"512",
"2"
] |
[
"nonn",
"tabl"
] | 78 | 0 | 3 |
[
"A000079",
"A009999",
"A040000",
"A047863",
"A135079",
"A320287",
"A355395",
"A355440"
] | null |
Seiichi Manyama, Jul 02 2022
| 2023-08-24T07:48:58 |
oeisdata/seq/A355/A355395.seq
|
87a6328c489f82dafbdd23fd37c5fe40
|
A355396
|
Expansion of e.g.f. exp(exp(3*x)/3 - exp(x) + 2/3).
|
[
"1",
"0",
"2",
"8",
"38",
"240",
"1782",
"14728",
"134598",
"1352800",
"14800502",
"174593848",
"2205456838",
"29676417680",
"423455081142",
"6381678299368",
"101217742764358",
"1684357485887680",
"29328589792496502",
"533062885681064088",
"10091434399407455558",
"198592474864415055600"
] |
[
"nonn"
] | 13 | 0 | 3 |
[
"A002874",
"A355378",
"A355396"
] | null |
Seiichi Manyama, Jun 30 2022
| 2022-07-10T07:48:08 |
oeisdata/seq/A355/A355396.seq
|
ba36f36ffbefbdf75a76c29992901d0f
|
A355397
|
Expansion of e.g.f. exp(exp(3*x)/3 + exp(2*x)/2 - 5/6).
|
[
"1",
"2",
"9",
"51",
"350",
"2799",
"25373",
"255854",
"2831177",
"34023919",
"440414146",
"6099346455",
"89873849705",
"1402403637418",
"23081230257449",
"399284248276827",
"7238080522101270",
"137125745341692863",
"2708536196071195365",
"55660194042713099510",
"1187724805063462045289"
] |
[
"nonn"
] | 12 | 0 | 2 |
[
"A355380",
"A355397"
] | null |
Seiichi Manyama, Jun 30 2022
| 2022-07-05T02:24:14 |
oeisdata/seq/A355/A355397.seq
|
5a54eec5ebca35185957a6251d73934c
|
A355398
|
Expansion of e.g.f. exp(exp(3*x)/3 - exp(2*x)/2 + 1/6).
|
[
"1",
"0",
"1",
"5",
"22",
"115",
"761",
"5880",
"49897",
"460045",
"4621366",
"50385555",
"590795217",
"7389964400",
"98105330961",
"1377426850805",
"20388005470582",
"317112889169555",
"5167636268318921",
"88001180739368680",
"1562559584723343417",
"28871671817796197885",
"554116841783123679446"
] |
[
"nonn"
] | 13 | 0 | 4 |
[
"A355381",
"A355398"
] | null |
Seiichi Manyama, Jun 30 2022
| 2022-07-05T02:24:19 |
oeisdata/seq/A355/A355398.seq
|
2c9efc51abcb778eeaa8ac7ed9ab2f84
|
A355399
|
a(n) is the failed skew zero forcing number of C^2_n.
|
[
"0",
"1",
"2",
"4",
"3",
"4",
"6",
"5",
"6",
"8",
"6",
"8",
"10",
"8",
"10",
"12",
"10",
"12",
"14",
"12",
"14",
"16",
"14",
"16",
"18",
"16",
"18",
"20",
"18",
"20",
"22",
"20",
"22",
"24",
"22",
"24",
"26",
"24",
"26",
"28",
"26",
"28",
"30",
"28",
"30",
"32",
"30",
"32",
"34",
"32",
"34",
"36",
"34",
"36",
"38",
"36",
"38",
"40",
"38",
"40",
"42",
"40",
"42",
"44",
"42",
"44",
"46",
"44",
"46"
] |
[
"nonn",
"easy"
] | 35 | 3 | 3 |
[
"A008611",
"A343648",
"A355399"
] | null |
Darren Narayan, Andrew E. Vick, and Aidan Johnson, Jun 30 2022
| 2025-03-28T11:28:34 |
oeisdata/seq/A355/A355399.seq
|
fc49a3090cbce49b00e873ac9aa016dc
|
A355400
|
Number of n-tuples (p_1, p_2, ..., p_n) of Dyck paths of semilength n, such that each p_i is never below p_{i-1}.
|
[
"1",
"1",
"3",
"30",
"1001",
"111384",
"41314284",
"51067020290",
"210309203300625",
"2885318087540733000",
"131857099297936066411200",
"20070377346929658409924542720",
"10174783866874800701945612292557712",
"17178820188393063395267380511228827387600",
"96592800670609299321035523895170598736583965100"
] |
[
"nonn"
] | 45 | 0 | 3 |
[
"A000108",
"A006125",
"A074962",
"A076113",
"A078920",
"A110131",
"A112332",
"A123352",
"A131577",
"A355400",
"A358597",
"A368025",
"A368298",
"A378113"
] | null |
Alois P. Heinz, Jun 30 2022
| 2024-11-16T19:13:57 |
oeisdata/seq/A355/A355400.seq
|
f342771f54d5b77ef428045bd6c48857
|
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