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1999-12-11 03:00:00
2025-04-28 00:58:08
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A357701
Irregular triangle read by rows where row n is the vertex depths of the rooted binary tree with Colijn-Plazzotta tree number n, traversed in pre-order, numerically larger child first.
[ "0", "0", "1", "1", "0", "1", "2", "2", "1", "0", "1", "2", "2", "1", "2", "2", "0", "1", "2", "3", "3", "2", "1", "0", "1", "2", "3", "3", "2", "1", "2", "2", "0", "1", "2", "3", "3", "2", "1", "2", "3", "3", "2", "0", "1", "2", "3", "3", "2", "3", "3", "1", "0", "1", "2", "3", "3", "2", "3", "3", "1", "2", "2", "0", "1", "2", "3", "3", "2", "3", "3", "1", "2", "3", "3", "2", "0", "1", "2", "3", "3", "2", "3", "3", "1", "2", "3", "3", "2", "3", "3" ]
[ "nonn", "easy", "tabf", "changed" ]
21
1
7
[ "A002024", "A002260", "A064002", "A357701", "A357702" ]
null
Kevin Ryde, Oct 11 2022
2025-04-22T19:11:25
oeisdata/seq/A357/A357701.seq
19f07d830fd687f638ec54aab017a0d6
A357702
Path length (total depths of vertices) of the rooted binary tree with Colijn-Plazzotta tree number n.
[ "0", "2", "6", "10", "12", "16", "22", "18", "22", "28", "34", "20", "24", "30", "36", "38", "26", "30", "36", "42", "44", "50", "34", "38", "44", "50", "52", "58", "66", "28", "32", "38", "44", "46", "52", "60", "54", "34", "38", "44", "50", "52", "58", "66", "60", "66", "42", "46", "52", "58", "60", "66", "74", "68", "74", "82", "50", "54", "60", "66", "68", "74", "82", "76", "82", "90" ]
[ "nonn", "easy" ]
9
1
2
[ "A002024", "A002260", "A064002", "A196047", "A357701", "A357702" ]
null
Kevin Ryde, Oct 11 2022
2024-12-19T11:46:19
oeisdata/seq/A357/A357702.seq
d402e51c4ddb2b38198dce5ec34fb826
A357703
Expansion of e.g.f. cosh( sqrt(3) * log(1-x) ).
[ "1", "0", "3", "9", "42", "240", "1614", "12474", "108900", "1059696", "11371932", "133410420", "1698541416", "23324023008", "343606235544", "5405580540360", "90445832210448", "1603781918563968", "30042007763367600", "592788643008571152", "12289695299276133024", "267079782474700715520" ]
[ "nonn" ]
20
0
3
[ "A357615", "A357703", "A357712" ]
null
Seiichi Manyama, Oct 10 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357703.seq
eab8ccbff925f01cc718a5997774d8c5
A357704
Triangle read by rows where T(n,k) is the number of reversed integer partitions of n with half-alternating sum k, where k ranges from -n to n in steps of 2.
[ "1", "0", "1", "0", "0", "2", "0", "0", "1", "2", "0", "0", "2", "0", "3", "0", "0", "2", "2", "0", "3", "0", "0", "3", "1", "3", "0", "4", "0", "0", "3", "2", "4", "2", "0", "4", "0", "0", "4", "2", "6", "2", "3", "0", "5", "0", "0", "4", "3", "5", "7", "3", "3", "0", "5", "0", "0", "5", "3", "8", "4", "10", "2", "4", "0", "6", "0", "0", "5", "4", "8", "6", "11", "9", "3", "4", "0", "6", "0", "0", "6", "4", "11", "5", "15", "8", "13", "3", "5", "0", "7" ]
[ "nonn", "tabl" ]
7
0
6
[ "A000041", "A008619", "A029862", "A035363", "A035544", "A053251", "A097805", "A344612", "A344651", "A351005", "A351006", "A357136", "A357189", "A357487", "A357488", "A357621", "A357623", "A357629", "A357630", "A357631", "A357632", "A357633", "A357634", "A357637", "A357638", "A357639", "A357640", "A357641", "A357643", "A357644", "A357645", "A357646", "A357704", "A357705" ]
null
Gus Wiseman, Oct 10 2022
2022-10-10T20:47:12
oeisdata/seq/A357/A357704.seq
47700521db33480d2af3a7a6898d80a2
A357705
Triangle read by rows where T(n,k) is the number of reversed integer partitions of n with skew-alternating sum k, where k ranges from -n to n in steps of 2.
[ "1", "0", "1", "0", "1", "1", "0", "2", "0", "1", "0", "2", "2", "0", "1", "0", "3", "1", "2", "0", "1", "0", "3", "2", "3", "2", "0", "1", "0", "4", "2", "4", "1", "3", "0", "1", "0", "4", "3", "3", "6", "2", "3", "0", "1", "0", "5", "3", "5", "3", "7", "2", "4", "0", "1", "0", "5", "4", "5", "4", "9", "7", "3", "4", "0", "1", "0", "6", "4", "7", "3", "12", "5", "10", "3", "5", "0", "1" ]
[ "nonn", "tabl" ]
6
0
8
[ "A000041", "A004526", "A035363", "A035594", "A053251", "A097805", "A298311", "A344651", "A351005", "A351006", "A357136", "A357189", "A357487", "A357488", "A357621", "A357623", "A357624", "A357629", "A357630", "A357631", "A357632", "A357633", "A357634", "A357636", "A357637", "A357638", "A357639", "A357640", "A357643", "A357644", "A357645", "A357646", "A357704", "A357705" ]
null
Gus Wiseman, Oct 10 2022
2022-10-10T20:47:08
oeisdata/seq/A357/A357705.seq
eb39b627388dc4293348f76ce419b5c3
A357706
Numbers k such that the k-th composition in standard order has half-alternating sum and skew-alternating sum both 0.
[ "0", "15", "45", "54", "59", "153", "170", "179", "204", "213", "230", "235", "247", "255", "561", "594", "611", "660", "677", "710", "715", "727", "735", "750", "765", "792", "809", "842", "851", "871", "879", "894", "908", "917", "934", "939", "951", "959", "973", "982", "987", "1005", "1014", "1019" ]
[ "nonn" ]
6
1
2
[ "A000583", "A001511", "A001700", "A004006", "A035363", "A035594", "A088218", "A228248", "A357136", "A357182", "A357625", "A357626", "A357627", "A357628", "A357631", "A357632", "A357636", "A357639", "A357640", "A357641", "A357642", "A357706" ]
null
Gus Wiseman, Oct 13 2022
2022-10-13T12:28:23
oeisdata/seq/A357/A357706.seq
47412dbdf9bf150714f6c0bf19732cd8
A357707
Numbers whose prime indices have equal number of parts congruent to each of 1 and 3 (mod 4).
[ "1", "3", "7", "9", "10", "13", "19", "21", "27", "29", "30", "34", "37", "39", "43", "49", "53", "55", "57", "61", "62", "63", "70", "71", "79", "81", "87", "89", "90", "91", "94", "100", "101", "102", "107", "111", "113", "115", "117", "129", "130", "131", "133", "134", "139", "147", "151", "159", "163", "165", "166", "169", "171", "173", "181", "183", "186", "187", "189" ]
[ "nonn" ]
7
1
2
[ "A035363", "A035544", "A035550", "A035594", "A053251", "A056239", "A066207", "A097805", "A112798", "A298311", "A316524", "A344616", "A344651", "A357486", "A357623", "A357632", "A357636", "A357638", "A357640", "A357704", "A357705", "A357707" ]
null
Gus Wiseman, Oct 12 2022
2022-10-12T19:44:51
oeisdata/seq/A357/A357707.seq
7eedfd8ce0579c1eb8edcd7131654887
A357708
Numbers k such that the k-th composition in standard order has sum equal to twice its maximum part.
[ "3", "10", "11", "13", "14", "36", "37", "38", "39", "41", "44", "50", "51", "52", "57", "60", "136", "137", "138", "139", "140", "141", "142", "143", "145", "152", "162", "163", "168", "177", "184", "196", "197", "198", "199", "200", "209", "216", "226", "227", "232", "241", "248", "528", "529", "530", "531", "532", "533", "534", "535", "536", "537", "538", "539" ]
[ "nonn" ]
6
1
1
[ "A000120", "A001511", "A003754", "A029931", "A066311", "A124767", "A329395", "A333766", "A333768", "A356844", "A357708" ]
null
Gus Wiseman, Oct 14 2022
2022-10-15T08:10:51
oeisdata/seq/A357/A357708.seq
c09e8bf3d9837a7d90af5dadb650d4ed
A357709
Number of integer partitions of n whose length is twice their alternating sum.
[ "1", "0", "0", "1", "0", "1", "1", "1", "2", "2", "4", "3", "6", "6", "9", "11", "13", "18", "21", "28", "32", "44", "49", "65", "76", "96", "114", "141", "170", "204", "250", "295", "361", "425", "516", "606", "734", "858", "1031", "1210", "1440", "1690", "2000", "2347", "2759", "3240", "3786", "4441", "5174", "6053", "7030", "8210", "9509", "11074", "12807", "14870" ]
[ "nonn" ]
5
0
9
[ "A000009", "A000041", "A004526", "A025047", "A097805", "A103919", "A262046", "A262977", "A301987", "A344651", "A357136", "A357182", "A357183", "A357184", "A357189", "A357485", "A357486", "A357488", "A357709", "A357847", "A357848" ]
null
Gus Wiseman, Oct 16 2022
2022-10-17T07:07:22
oeisdata/seq/A357/A357709.seq
2e3be1efb9ad312747fe15b390539b19
A357710
Number of integer compositions of n with integer geometric mean.
[ "0", "1", "2", "2", "3", "4", "4", "8", "4", "15", "17", "22", "48", "40", "130", "88", "287", "323", "543", "1084", "1145", "2938", "3141", "6928", "9770", "15585", "29249", "37540", "78464", "103289", "194265", "299752", "475086", "846933", "1216749", "2261920", "3320935", "5795349", "9292376", "14825858", "25570823", "39030115", "68265801", "106030947", "178696496" ]
[ "nonn" ]
15
0
3
[ "A011782", "A025047", "A051293", "A067538", "A067539", "A078174", "A078175", "A102627", "A271654", "A320322", "A326027", "A326028", "A326622", "A326623", "A326624", "A326625", "A326641", "A339452", "A357182", "A357183", "A357490", "A357710" ]
null
Gus Wiseman, Oct 15 2022
2023-09-24T13:03:43
oeisdata/seq/A357/A357710.seq
33ced8cac424b7f4612200f58e435dc6
A357711
Expansion of e.g.f. cosh( 2 * log(1-x) ).
[ "1", "0", "4", "12", "60", "360", "2520", "20160", "181440", "1814400", "19958400", "239500800", "3113510400", "43589145600", "653837184000", "10461394944000", "177843714048000", "3201186852864000", "60822550204416000", "1216451004088320000", "25545471085854720000", "562000363888803840000" ]
[ "nonn" ]
14
0
3
[ "A065143", "A357711", "A357712" ]
null
Seiichi Manyama, Oct 10 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357711.seq
c2cd8ad653ff1c74abdbe3f7839b4646
A357712
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. cosh( sqrt(k) * log(1-x) ).
[ "1", "1", "0", "1", "0", "0", "1", "0", "1", "0", "1", "0", "2", "3", "0", "1", "0", "3", "6", "12", "0", "1", "0", "4", "9", "26", "60", "0", "1", "0", "5", "12", "42", "140", "360", "0", "1", "0", "6", "15", "60", "240", "896", "2520", "0", "1", "0", "7", "18", "80", "360", "1614", "6636", "20160", "0", "1", "0", "8", "21", "102", "500", "2520", "12474", "55804", "181440", "0", "1", "0", "9", "24", "126", "660", "3620", "20160", "108900", "525168", "1814400", "0" ]
[ "nonn", "tabl" ]
18
0
13
[ "A000007", "A105752", "A263687", "A357681", "A357683", "A357703", "A357711", "A357712" ]
null
Seiichi Manyama, Oct 10 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357712.seq
57cf336e3f81806845190e470cba6979
A357713
a(0) = 2; afterwards a(n) is the least prime greater than a(n-1) such that Omega(a(n-1) + a(n)) = n.
[ "2", "3", "7", "11", "13", "19", "197", "251", "389", "1531", "2053", "3067", "17669", "25339", "66821", "105211", "140549", "318203", "1008901", "1940219", "6710533", "9804539", "12215557", "34970363", "49964293", "75864827", "276456709", "864393979", "1350198533", "2877659899", "4101661957", "7709498107", "16449692933", "51196041979" ]
[ "nonn" ]
28
0
1
[ "A001222", "A357713" ]
null
Zak Seidov, Oct 10 2022
2023-09-25T08:15:24
oeisdata/seq/A357/A357713.seq
2511b5c0471322245e0a686eaea81f83
A357714
a(n) is the number of equations in the set E_{n,b} := {x+2^b*y=n^b, 2^b*x+3^b*y=n^b, ..., k^b*x+(k+1)^b*y=n^b, ..., n^b*x+(n+1)^b*y=n^b} which admit at least one nonnegative integer solution when b is sufficiently large.
[ "1", "2", "3", "4", "3", "5", "4", "6", "5", "6", "4", "8", "5", "7", "7", "8", "5", "9", "5", "9", "8", "8", "6", "12", "7", "8", "8", "10", "6", "12", "7", "11", "9", "9", "9", "14", "7", "9", "9", "13", "7", "13", "8", "12", "12", "10", "8", "16", "9", "12", "10", "12", "8", "14", "10", "14", "11", "11", "9", "19", "9", "11", "13", "14", "11", "15", "9", "13", "11", "15", "9", "19", "10", "12", "14", "14", "12", "16", "10", "18", "13" ]
[ "nonn" ]
13
1
2
[ "A000005", "A356770", "A357714" ]
null
Luca Onnis, Oct 10 2022
2022-12-11T10:19:37
oeisdata/seq/A357/A357714.seq
918887f22b080135594f9432ec967112
A357715
Decimal expansion of sqrt(16 + 32 / sqrt(5)).
[ "5", "5", "0", "5", "5", "2", "7", "6", "8", "1", "8", "8", "4", "6", "9", "4", "1", "5", "2", "8", "2", "8", "8", "3", "8", "3", "2", "7", "6", "4", "3", "5", "5", "0", "7", "1", "8", "1", "0", "3", "5", "9", "7", "3", "4", "4", "0", "3", "2", "6", "3", "4", "6", "5", "3", "4", "6", "2", "7", "0", "3", "0", "6", "2", "4", "7", "6", "3", "8", "0", "7", "7", "5", "0", "6", "8", "6", "9", "1", "9", "4", "0", "2", "6", "3", "8", "1", "1", "9", "7", "2", "4", "4", "0", "2", "8", "0" ]
[ "nonn", "cons", "easy" ]
27
1
1
[ "A019934", "A019952", "A019970", "A121570", "A179290", "A204188", "A356869", "A357715" ]
null
Michal Paulovic, Oct 10 2022
2022-11-17T05:31:10
oeisdata/seq/A357/A357715.seq
05e907ed0feda020d6ca91ac51164166
A357716
Number of ways to write n as an ordered sum of eight positive Fibonacci numbers (with a single type of 1).
[ "1", "8", "36", "112", "274", "560", "1008", "1640", "2479", "3536", "4844", "6392", "8170", "10136", "12308", "14680", "17291", "20160", "23248", "26440", "29674", "32992", "36456", "40040", "43834", "47712", "51752", "55840", "60250", "64856", "69560", "74088", "78331", "82440", "86500", "90616", "95074", "99568", "104188", "108528", "113304" ]
[ "nonn" ]
6
8
2
[ "A000045", "A076739", "A121548", "A121549", "A121550", "A319401", "A357688", "A357690", "A357691", "A357694", "A357716", "A357717" ]
null
Ilya Gutkovskiy, Oct 10 2022
2022-10-10T16:11:09
oeisdata/seq/A357/A357716.seq
2dc1ae842135452ff823abb55ed83cf1
A357717
Number of ways to write n as an ordered sum of nine positive Fibonacci numbers (with a single type of 1).
[ "1", "9", "45", "156", "423", "954", "1878", "3321", "5409", "8251", "11979", "16686", "22446", "29250", "37134", "46107", "56259", "67671", "80407", "94338", "109269", "125118", "141930", "159723", "178608", "198522", "219510", "241338", "264438", "288810", "314550", "341010", "367785", "394596", "421443", "448650", "476614", "505404", "534978" ]
[ "nonn" ]
6
9
2
[ "A000045", "A076739", "A121548", "A121549", "A121550", "A319402", "A357688", "A357690", "A357691", "A357694", "A357716", "A357717" ]
null
Ilya Gutkovskiy, Oct 10 2022
2022-10-10T16:11:15
oeisdata/seq/A357/A357717.seq
e5af850941548994ee23fdb6e96ea7dd
A357718
Expansion of e.g.f. cos( sqrt(3) * log(1+x) ).
[ "1", "0", "-3", "9", "-24", "60", "-84", "-756", "13104", "-157248", "1795248", "-20900880", "254007936", "-3250473408", "43922668608", "-626830626240", "9437477107968", "-149644407564288", "2493958878657792", "-43592393744250624", "797394015216175104", "-15230735270523601920" ]
[ "sign" ]
12
0
3
[ "A357703", "A357718", "A357720", "A357726" ]
null
Seiichi Manyama, Oct 10 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357718.seq
0ece697eb794186e333c1d7609e0c5e8
A357719
Expansion of e.g.f. cos( 2 * log(1+x) ).
[ "1", "0", "-4", "12", "-28", "40", "200", "-3360", "35680", "-357120", "3644800", "-38896000", "437756800", "-5206406400", "65372153600", "-864339840000", "11991424640000", "-173800340480000", "2617640829440000", "-40693929269760000", "647089190924800000", "-10383194262604800000" ]
[ "sign" ]
11
0
3
[ "A357711", "A357719", "A357720", "A357727" ]
null
Seiichi Manyama, Oct 10 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357719.seq
a5f7b61b479288820eefc1804c4cdec6
A357720
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. cos( sqrt(k) * log(1+x) ).
[ "1", "1", "0", "1", "0", "0", "1", "0", "-1", "0", "1", "0", "-2", "3", "0", "1", "0", "-3", "6", "-10", "0", "1", "0", "-4", "9", "-18", "40", "0", "1", "0", "-5", "12", "-24", "60", "-190", "0", "1", "0", "-6", "15", "-28", "60", "-216", "1050", "0", "1", "0", "-7", "18", "-30", "40", "-84", "756", "-6620", "0", "1", "0", "-8", "21", "-30", "0", "200", "-756", "-1620", "46800", "0", "1", "0", "-9", "24", "-28", "-60", "630", "-3360", "13104", "-14256", "-365300", "0" ]
[ "sign", "tabl" ]
12
0
13
[ "A000007", "A003703", "A357693", "A357712", "A357718", "A357719", "A357720", "A357721", "A357728" ]
null
Seiichi Manyama, Oct 10 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357720.seq
cab5a61d88f9e9e1e25d07ecb24c64cd
A357721
a(n) = Sum_{k=0..floor(n/2)} (-n)^k * Stirling1(n,2*k).
[ "1", "0", "-2", "9", "-28", "0", "1200", "-16464", "167904", "-1393200", "7429240", "43124400", "-2404571904", "55590286752", "-1027511503200", "16489054310400", "-222885864448000", "1994839594780032", "14489184835474272", "-1470395490046560000", "54581408106475622400", "-1608207353670788640000" ]
[ "sign" ]
10
0
3
[ "A357683", "A357720", "A357721", "A357729" ]
null
Seiichi Manyama, Oct 10 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357721.seq
926d1ad1becc8c804385b03ded780a5b
A357722
Number of partitions of n into 4 distinct positive Fibonacci numbers (with a single type of 1).
[ "1", "0", "0", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "2", "1", "2", "2", "2", "2", "1", "2", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "2", "1", "2", "2", "2", "2", "1", "2", "2", "2", "3", "1", "2", "1", "1", "2", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "2", "1", "2", "2", "1", "3", "2", "2", "2" ]
[ "nonn" ]
12
11
17
[ "A000045", "A000119", "A319397", "A357688", "A357722", "A357731", "A357732" ]
null
Ilya Gutkovskiy, Oct 11 2022
2022-10-24T00:00:03
oeisdata/seq/A357/A357722.seq
bde7e9a00f81270d99d9a6d524b8e20b
A357723
Number of ways to place a non-attacking black king and white king on an n X n board, up to rotation and reflection.
[ "0", "0", "0", "5", "21", "63", "135", "270", "462", "770", "1170", "1755", "2475", "3465", "4641", "6188", "7980", "10260", "12852", "16065", "19665", "24035", "28875", "34650", "40986", "48438", "56550", "65975", "76167", "87885", "100485", "114840", "130200", "147560", "166056", "186813", "208845", "233415", "259407", "288230", "318630" ]
[ "nonn", "easy" ]
51
0
4
[ "A035286", "A279111", "A357723", "A357740" ]
null
Nathan L. Skirrow, Oct 10 2022
2023-02-02T16:10:48
oeisdata/seq/A357/A357723.seq
d66e4891a9a9f231051fd719daa09e83
A357724
Triangular array read by rows: T(n,k) = Fib(n) mod Fib(k) for 1 <= k <= n, where Fib(k) = A000045(k).
[ "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "1", "2", "0", "0", "0", "0", "2", "3", "0", "0", "0", "1", "1", "3", "5", "0", "0", "0", "1", "0", "1", "5", "8", "0", "0", "0", "0", "1", "4", "2", "8", "13", "0", "0", "0", "1", "1", "0", "7", "3", "13", "21", "0", "0", "0", "1", "2", "4", "1", "11", "5", "21", "34", "0", "0", "0", "0", "0", "4", "0", "1", "18", "8", "34", "55", "0", "0", "0", "1", "2", "3", "1", "12", "2", "29", "13", "55", "89", "0", "0", "0", "1", "2" ]
[ "nonn", "look", "tabl" ]
32
1
14
[ "A000045", "A357724", "A357814" ]
null
J. M. Bergot and Robert Israel, Oct 12 2022
2022-10-23T23:12:54
oeisdata/seq/A357/A357724.seq
ceb980ae516ecff8850c587007dc87c3
A357725
Expansion of e.g.f. cos( sqrt(2) * (exp(x) - 1) ).
[ "1", "0", "-2", "-6", "-10", "10", "190", "1106", "4438", "9978", "-35250", "-666622", "-5657370", "-35308182", "-155215970", "-128513870", "7051468022", "105057922906", "1042016038254", "8053738122466", "44608555196294", "48639210067658", "-3200193654245442", "-60669816166988654", "-769281697485061994" ]
[ "sign" ]
24
0
3
[ "A121867", "A264036", "A357725", "A357728", "A357736" ]
null
Seiichi Manyama, Oct 10 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357725.seq
a70ae32a155e75ce9e03693236d84d46
A357726
Expansion of e.g.f. cos( sqrt(3) * (exp(x) - 1) ).
[ "1", "0", "-3", "-9", "-12", "45", "465", "2394", "7827", "639", "-250410", "-2588553", "-17773635", "-84525480", "-105849399", "3569654115", "56100280308", "561682625769", "4227837863181", "20472943653306", "-38990802816489", "-2621206974761253", "-42512769453705474", "-495174030273565173" ]
[ "sign" ]
24
0
3
[ "A357615", "A357726", "A357728", "A357737" ]
null
Seiichi Manyama, Oct 10 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357726.seq
db0f99846d38c117a87eee5f7091bd6e
A357727
Expansion of e.g.f. cos( 2 * (exp(x) - 1) ).
[ "1", "0", "-4", "-12", "-12", "100", "852", "4004", "9940", "-36828", "-726316", "-6174300", "-35968812", "-109708508", "702818004", "16677814436", "188794428628", "1542659688996", "8359981681364", "-3068614764636", "-868989327994668", "-15076627082974940", "-179727483880747308" ]
[ "sign" ]
23
0
3
[ "A065143", "A357719", "A357727", "A357728", "A357738" ]
null
Seiichi Manyama, Oct 10 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357727.seq
02e5343174e9ac735e5cc89843583e19
A357728
Square array T(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. cos( sqrt(k) * (exp(x) - 1) ).
[ "1", "1", "0", "1", "0", "0", "1", "0", "-1", "0", "1", "0", "-2", "-3", "0", "1", "0", "-3", "-6", "-6", "0", "1", "0", "-4", "-9", "-10", "-5", "0", "1", "0", "-5", "-12", "-12", "10", "33", "0", "1", "0", "-6", "-15", "-12", "45", "190", "266", "0", "1", "0", "-7", "-18", "-10", "100", "465", "1106", "1309", "0", "1", "0", "-8", "-21", "-6", "175", "852", "2394", "4438", "4905", "0", "1", "0", "-9", "-24", "0", "270", "1345", "4004", "7827", "9978", "11516", "0" ]
[ "sign", "tabl" ]
20
0
13
[ "A000007", "A121867", "A357681", "A357720", "A357725", "A357726", "A357727", "A357728", "A357729" ]
null
Seiichi Manyama, Oct 11 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357728.seq
c6b069c86b3d01f4be0213a026cdc334
A357729
a(n) = Sum_{k=0..floor(n/2)} (-n)^k * Stirling2(n,2*k).
[ "1", "0", "-2", "-9", "-12", "175", "1938", "9506", "-24248", "-1065663", "-12021610", "-56195425", "677072220", "19979234080", "251733387514", "1135594212255", "-29317384858352", "-901607623649489", "-13233854770928514", "-68574233644270566", "2258648937829442660", "81748108921355457777" ]
[ "sign" ]
19
0
3
[ "A357682", "A357721", "A357728", "A357729" ]
null
Seiichi Manyama, Oct 11 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357729.seq
46247e4e02fe39ebb1f625a9ba03dd6f
A357730
Number of ways to write n as an ordered sum of ten positive Fibonacci numbers (with a single type of 1).
[ "1", "10", "55", "210", "625", "1542", "3300", "6310", "11040", "17980", "27673", "40660", "57475", "78520", "104175", "134742", "170620", "212220", "260035", "314290", "374933", "441790", "514855", "594210", "680070", "772582", "871920", "977790", "1090680", "1210960", "1339417", "1475340", "1618020", "1766080", "1918785", "2076012" ]
[ "nonn" ]
6
10
2
[ "A000045", "A076739", "A121548", "A121549", "A121550", "A319403", "A357688", "A357690", "A357691", "A357694", "A357716", "A357717", "A357730" ]
null
Ilya Gutkovskiy, Oct 11 2022
2022-10-11T06:00:13
oeisdata/seq/A357/A357730.seq
d302a513a769e7a71121511c4e0aebad
A357731
Number of partitions of n into 2 distinct positive Fibonacci numbers (with a single type of 1).
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "0", "0", "1", "1", "1", "1", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "1", "1", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "1", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "1", "1", "0", "1" ]
[ "nonn" ]
9
3
null
[ "A000045", "A000119", "A121549", "A319395", "A357722", "A357731", "A357732" ]
null
Ilya Gutkovskiy, Oct 11 2022
2022-10-24T00:00:21
oeisdata/seq/A357/A357731.seq
5dcdf3d696a532b73efcce494fe3a68d
A357732
Number of partitions of n into 3 distinct positive Fibonacci numbers (with a single type of 1).
[ "1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "0", "1", "1", "1", "2", "1", "2", "1", "1", "2", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "0", "0", "1", "1", "1", "2", "1", "2", "1", "1", "2", "1", "1", "1", "0", "2", "1", "1", "1", "0", "1", "0", "0", "1", "1", "1", "1", "0", "1", "0", "0", "1", "0", "0", "0", "0", "1", "1", "1", "2", "1", "2" ]
[ "nonn" ]
6
6
11
[ "A000045", "A000119", "A121550", "A319396", "A357722", "A357731", "A357732" ]
null
Ilya Gutkovskiy, Oct 11 2022
2022-10-24T00:00:30
oeisdata/seq/A357/A357732.seq
5d836dff59f7ec91143a510761ffa9e4
A357733
Integer lengths of the sides of such regular hexagons that a polyline described in A356047 exists.
[ "1", "2", "286", "299", "56653", "56834", "11006686", "11009207", "2135467321", "2135502434", "414272813758", "414273302819", "80366834417221", "80366841228962", "15590752217183806", "15590752312059119", "3024525571838019313", "3024525573159461954", "586742370303288400606", "586742370321693722267", "113824995314922590647741" ]
[ "nonn", "easy" ]
19
1
2
[ "A356047", "A357733" ]
null
Alexander M. Domashenko, Oct 11 2022
2023-03-13T11:57:23
oeisdata/seq/A357/A357733.seq
3521300221e47659aa18e9a59d92b534
A357734
Array T(n,k), read by descending antidiagonals, whose rows are numbers congruent to p or q mod r, with 0 <= p < q < r, sorted by r, then p, then q.
[ "0", "1", "0", "2", "1", "0", "3", "3", "2", "1", "4", "4", "3", "2", "0", "5", "6", "5", "4", "1", "0", "6", "7", "6", "5", "4", "2", "0", "7", "9", "8", "7", "5", "4", "3", "1", "8", "10", "9", "8", "8", "6", "4", "2", "1", "9", "12", "11", "10", "9", "8", "7", "5", "3", "2", "10", "13", "12", "11", "12", "10", "8", "6", "5", "3", "0", "11", "15", "14", "13", "13", "12", "11", "9", "7", "6", "1", "0" ]
[ "nonn", "tabl", "easy" ]
27
1
4
[ "A144629", "A357734" ]
null
David Lovler, Oct 11 2022
2022-11-05T08:19:03
oeisdata/seq/A357/A357734.seq
c162ea44519acf2722fee5f97890e4eb
A357735
a(1)=1, a(2)=2. Thereafter a(n+1) is least k != partial sum s(n) which has not occurred earlier, such that gcd(k, s(n)) > 1.
[ "1", "2", "6", "3", "4", "8", "9", "11", "10", "12", "14", "5", "15", "16", "18", "20", "7", "21", "13", "24", "27", "22", "26", "28", "23", "25", "30", "32", "33", "31", "34", "35", "40", "44", "55", "36", "37", "39", "17", "42", "45", "38", "46", "48", "50", "19", "57", "52", "41", "62", "43", "54", "56", "58", "60", "64", "51", "63", "66", "49", "70", "77", "68", "69", "72", "75", "74", "76" ]
[ "nonn" ]
10
1
2
[ "A064413", "A084385", "A347113", "A351743", "A357735" ]
null
David James Sycamore, Oct 11 2022
2022-10-12T09:49:31
oeisdata/seq/A357/A357735.seq
deb0e1f781a3bf6b46e4401e9efb2244
A357736
Expansion of e.g.f. sin( sqrt(2) * (exp(x) - 1) )/sqrt(2).
[ "0", "1", "1", "-1", "-11", "-45", "-119", "-49", "2045", "18075", "105121", "436471", "679669", "-10538333", "-155858247", "-1404609569", "-9667430739", "-46708291093", "-25694453615", "3002522206471", "49051481154341", "546022210068595", "4800733688293929", "31399017314213487", "75507020603213405" ]
[ "sign" ]
17
0
5
[ "A264037", "A357725", "A357736" ]
null
Seiichi Manyama, Oct 11 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357736.seq
45667958485b32c7be580b6ad63c7d8f
A357737
Expansion of e.g.f. sin( sqrt(3) * (exp(x) - 1) )/sqrt(3).
[ "0", "1", "1", "-2", "-17", "-65", "-134", "331", "5797", "41092", "199621", "500731", "-2996432", "-58995155", "-573624323", "-4065029714", "-19194210269", "7657775035", "1581081323122", "24363365708815", "260409006907921", "2127851409822892", "11143555796154673", "-27234657667343081" ]
[ "sign" ]
16
0
4
[ "A357572", "A357726", "A357737" ]
null
Seiichi Manyama, Oct 11 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357737.seq
dfeff1ec05e199db62fb04909672828d
A357738
Expansion of e.g.f. sin( 2 * (exp(x) - 1) )/2.
[ "0", "1", "1", "-3", "-23", "-83", "-119", "973", "11145", "69805", "278281", "33165", "-12794231", "-157150355", "-1271714807", "-7108146611", "-11364216951", "380051588653", "6923479542025", "78935931180813", "669998027706505", "3602978599128301", "-8825050911646199", "-598024924863875123" ]
[ "sign" ]
18
0
4
[ "A357598", "A357727", "A357738" ]
null
Seiichi Manyama, Oct 11 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357738.seq
f9e1996d5e4eb790861fb363df8d2694
A357739
a(n) = Sum_{k=0..floor((n-1)/2)} (-n)^k * Stirling2(n,2*k+1).
[ "0", "1", "1", "-2", "-23", "-99", "1", "4411", "45137", "205570", "-1270799", "-38876573", "-441073511", "-1921300835", "34908578433", "994442615986", "13032718992033", "59450652771077", "-1794250960044623", "-57608157168424497", "-901446808420344919", "-5274602459214885362", "160827105304127790529" ]
[ "sign" ]
11
0
4
null
null
Seiichi Manyama, Oct 11 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357739.seq
97de43c49fbf544ca8bbdb4d02ec29b3
A357740
Number of non-equivalent ways under symmetry in one axis that 2 non-attacking kings of different colors can be placed on an n X n board.
[ "0", "0", "17", "78", "234", "520", "1035", "1806", "2996", "4608", "6885", "9790", "13662", "18408", "24479", "31710", "40680", "51136", "63801", "78318", "95570", "115080", "137907", "163438", "192924", "225600", "262925", "303966", "350406", "401128", "458055", "519870", "588752", "663168", "745569", "834190", "931770", "1036296", "1150811", "1273038" ]
[ "nonn", "easy" ]
29
1
3
[ "A035286", "A357723", "A357740" ]
null
Nathan L. Skirrow, Oct 11 2022
2023-04-03T21:47:29
oeisdata/seq/A357/A357740.seq
d9435aff2ee74bcefc937a8b305976eb
A357741
Semiprimes k such that k is divisible by its index in the sequence of semiprimes.
[ "4", "6", "9", "21", "33", "129", "159", "3066835", "3067195", "3067255", "3067615", "3067745", "3068045", "44690978227", "44690978647", "44690978983", "44690979529" ]
[ "nonn", "hard", "more" ]
56
1
1
[ "A001358", "A106125", "A356764", "A357741" ]
null
Lucas A. Brown, Oct 13 2022
2022-10-29T04:42:53
oeisdata/seq/A357/A357741.seq
23eb39baf445c4595d651a1a61b48e56
A357742
a(n) is the maximum binary weight of the squares of n-bit numbers.
[ "1", "2", "3", "5", "6", "8", "9", "13", "13", "15", "16", "18", "20", "22", "24", "25", "27", "29", "31", "34", "34", "37", "38", "39", "41", "44", "44", "47", "49", "51", "52", "54", "55", "57", "59", "63", "63", "64", "66", "68", "69", "72", "73", "76", "77", "78", "80", "82", "85", "87" ]
[ "nonn", "base", "hard", "more" ]
26
1
2
[ "A000290", "A159918", "A357304", "A357658", "A357742" ]
null
Karl-Heinz Hofmann and Hugo Pfoertner , Oct 11 2022
2023-12-26T03:52:06
oeisdata/seq/A357/A357742.seq
f9c6f7805267e7d3c8981b2b3c063609
A357743
Square array A(n, k), n, k >= 0, read by antidiagonals: A(0, 0) = 0, A(0, 1) = A(1, 0) = 1, for n, k >= 0, A(2*n, 2*k) = A(n, k), A(2*n, 2*k+1) = A(n, k) + A(n, k+1), A(2*n+1, 2*k) = A(n, k) + A(n+1, k), A(2*n+1, 2*k+1) = A(n, k+1) + A(n+1, k).
[ "0", "1", "1", "1", "2", "1", "2", "3", "3", "2", "1", "3", "2", "3", "1", "3", "4", "5", "5", "4", "3", "2", "5", "3", "6", "3", "5", "2", "3", "5", "6", "5", "5", "6", "5", "3", "1", "4", "3", "5", "2", "5", "3", "4", "1", "4", "5", "7", "8", "7", "7", "8", "7", "5", "4", "3", "7", "4", "9", "5", "10", "5", "9", "4", "7", "3", "5", "8", "9", "7", "8", "11", "11", "8", "7", "9", "8", "5", "2", "7", "5", "8", "3", "9", "6", "9", "3", "8", "5", "7", "2" ]
[ "nonn", "tabl" ]
52
0
5
[ "A002487", "A007306", "A355855", "A357743", "A358871" ]
null
Rémy Sigrist, Nov 29 2022
2022-12-05T20:46:31
oeisdata/seq/A357/A357743.seq
75dbf3ccf2d764697d48b66e79d5dd4f
A357744
a(n) is the least k such that prime(n) * k occurs in one of the eight main spokes of a square spiral with 1 in the center.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "4", "1", "1", "25", "1", "17", "1", "59", "1", "13", "37", "1", "4", "3", "13", "5", "1", "21", "8", "2", "4", "1", "131", "3", "1", "2", "1", "1", "1", "2", "37", "4", "13", "58", "7", "1", "34", "1", "7", "23", "4", "1", "29", "1", "251", "1", "5", "25", "3", "13", "1", "7", "30", "1", "311", "31", "38", "3", "49", "3", "6", "5", "37", "19", "16", "7", "5", "149", "3", "1", "7", "419", "1", "1", "91", "10", "2" ]
[ "nonn" ]
56
1
10
[ "A000040", "A016754", "A033951", "A053755", "A054552", "A054554", "A054556", "A054567", "A054569", "A357744", "A357745" ]
null
Karl-Heinz Hofmann, Dec 01 2022
2023-01-31T08:25:37
oeisdata/seq/A357/A357744.seq
45c2a8dfc7da45a48d8b1cb0c2d3302c
A357745
Numbers on the 8 main spokes of a square spiral with 1 in the center.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "11", "13", "15", "17", "19", "21", "23", "25", "28", "31", "34", "37", "40", "43", "46", "49", "53", "57", "61", "65", "69", "73", "77", "81", "86", "91", "96", "101", "106", "111", "116", "121", "127", "133", "139", "145", "151", "157", "163", "169", "176", "183", "190", "197", "204", "211", "218", "225", "233", "241", "249", "257", "265", "273" ]
[ "nonn", "easy" ]
43
1
2
[ "A002061", "A016754", "A033951", "A039823", "A053755", "A054552", "A054554", "A054556", "A054567", "A054569", "A080335", "A200975", "A267682", "A317186", "A357745" ]
null
Karl-Heinz Hofmann, Dec 22 2022
2023-06-16T05:30:13
oeisdata/seq/A357/A357745.seq
774adc6d8943efb8fd4cf442d6231df9
A357746
Primes p such that the least k for which k*p + 1 is prime is also the least k for which k*p - 1 is prime.
[ "47", "103", "107", "283", "313", "347", "397", "773", "787", "907", "1051", "1117", "1319", "1433", "1823", "2027", "2153", "2203", "2287", "2333", "2347", "2381", "2909", "3221", "3257", "3673", "3923", "3929", "4129", "4153", "4217", "4547", "4597", "4657", "4721", "4969", "5023", "5387", "5407", "5693", "5717", "5827", "5881", "6373", "6781", "6863", "6997" ]
[ "nonn" ]
16
1
1
[ "A000040", "A001359", "A006512", "A014574", "A035096", "A216568", "A357746" ]
null
Karl-Heinz Hofmann, Jan 01 2023
2023-01-02T15:26:50
oeisdata/seq/A357/A357746.seq
68f73ca62937d5bf600193677561a301
A357747
Distances in the lyrics of the Rolling Stones song "2000 Light Years From Home".
[ "100", "600", "1000", "2000" ]
[ "nonn", "fini", "full", "less" ]
8
1
1
[ "A357747", "A357748" ]
null
Hugo Pfoertner, Oct 15 2022
2022-10-15T20:21:17
oeisdata/seq/A357/A357747.seq
c1d7527609ebd7a8a1490bc69d0a79e5
A357748
Numbers in the lyrics of the Rolling Stones song "2000 Light Years From Home" in the order in which they appear.
[ "100", "600", "1000", "1000", "14", "2000", "2000" ]
[ "nonn", "fini", "full", "less" ]
6
1
1
[ "A357747", "A357748" ]
null
Hugo Pfoertner, Oct 15 2022
2022-10-15T20:21:47
oeisdata/seq/A357/A357748.seq
467b485ce3d654fd8d8cb94c2bc80a12
A357749
Sorted list of nonzero numbers x, y, z that occur in solutions to the equation (x + y)^2 + (y + z)^2 + (z + x)^2 = 12*x*y*z.
[ "1", "3", "13", "61", "217", "291", "1393", "3673", "4683", "6673", "16693", "31971", "62221", "106153", "153181", "360517", "733933", "1054081", "1285131", "1709221", "2430493", "3516483", "4778353", "16848481", "17857153", "21717363", "27755113", "38745493", "55764867", "80725921", "98938381", "185236633", "302517517", "386781123" ]
[ "nonn" ]
11
1
2
[ "A002559", "A101368", "A357749", "A357870" ]
null
Hugo Pfoertner, Oct 18 2022
2022-10-18T13:50:53
oeisdata/seq/A357/A357749.seq
9e7145b2a7915fc6e6675bdf0a0a0b25
A357750
a(n) is the least k such that B(k^2) - B(k) = n, where B(m) is the binary weight A000120(m).
[ "0", "5", "11", "21", "45", "75", "217", "331", "181", "789", "1241", "2505", "5701", "5221", "11309", "19637", "43151", "69451", "82709", "166027", "346389", "607307", "689685", "1458357", "1380917", "2507541", "5906699", "2965685", "5931189", "11862197", "47448787", "82188309", "57804981", "94905541", "188883211", "373457573", "640164021" ]
[ "nonn", "base" ]
21
0
2
[ "A000120", "A000290", "A159918", "A164343", "A164344", "A356877", "A357658", "A357750" ]
null
Karl-Heinz Hofmann and Hugo Pfoertner, Oct 17 2022
2025-01-03T18:39:46
oeisdata/seq/A357/A357750.seq
ebdfe77a26b4f368514bc1d622cec636
A357751
a(n) is the least perfect power > 2^n.
[ "4", "4", "8", "9", "25", "36", "81", "144", "289", "529", "1089", "2116", "4225", "8281", "16641", "33124", "66049", "131769", "263169", "525625", "1050625", "2099601", "4198401", "8392609", "16785409", "33558849", "67125249", "134235396", "268468225", "536895241", "1073807361", "2147488281", "4295098369", "8589953124", "17180131329", "34359812496" ]
[ "nonn", "easy" ]
14
0
1
[ "A000079", "A001597", "A357751", "A357752" ]
null
Hugo Pfoertner, Oct 12 2022
2022-10-13T13:08:28
oeisdata/seq/A357/A357751.seq
bd77110e2d42c30a03dd65f8154844a3
A357752
a(n) is the largest perfect power < 2^n.
[ "4", "9", "27", "49", "125", "243", "484", "1000", "2025", "3969", "8100", "16129", "32761", "65025", "131044", "261121", "524176", "1046529", "2096704", "4190209", "8386816", "16769025", "33547264", "67092481", "134212225", "268402689", "536848900", "1073676289", "2147395600", "4294836225", "8589767761", "17179607041", "34359441769" ]
[ "nonn" ]
6
3
1
[ "A000079", "A001597", "A357751", "A357752", "A357754" ]
null
Hugo Pfoertner, Oct 12 2022
2022-10-12T08:59:53
oeisdata/seq/A357/A357752.seq
428e352dfbc087e751d0fdea47a9aeb0
A357753
a(n) is the least square with n binary digits.
[ "4", "9", "16", "36", "64", "144", "256", "529", "1024", "2116", "4096", "8281", "16384", "33124", "65536", "131769", "262144", "525625", "1048576", "2099601", "4194304", "8392609", "16777216", "33558849", "67108864", "134235396", "268435456", "536895241", "1073741824", "2147488281", "4294967296", "8589953124", "17179869184" ]
[ "nonn", "base" ]
36
3
1
[ "A000290", "A000302", "A017912", "A065732", "A070939", "A357753", "A357754" ]
null
Hugo Pfoertner, Oct 11 2022
2022-10-18T13:31:31
oeisdata/seq/A357/A357753.seq
0f67e7a5c1d69a7dd70834c81eb4a956
A357754
a(n) is the largest square with n binary digits.
[ "4", "9", "25", "49", "121", "225", "484", "961", "2025", "3969", "8100", "16129", "32761", "65025", "131044", "261121", "524176", "1046529", "2096704", "4190209", "8386816", "16769025", "33547264", "67092481", "134212225", "268402689", "536848900", "1073676289", "2147395600", "4294836225", "8589767761", "17179607041", "34359441769" ]
[ "nonn", "base", "easy" ]
25
3
1
[ "A000290", "A056007", "A070939", "A116601", "A357753", "A357754" ]
null
Hugo Pfoertner, Oct 11 2022
2022-10-13T15:27:58
oeisdata/seq/A357/A357754.seq
e31cac169e29f184d2f83ad7abfddd71
A357755
Number of solutions for a 10-digit number whose n-th power contains each digit (0-9) exactly n times.
[ "3265920", "468372", "65663", "15487", "5020", "1930", "855", "417", "246", "114", "97", "45", "33", "24", "20", "18", "7", "6", "1", "3", "2", "3", "0", "1", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "1" ]
[ "nonn", "base", "more" ]
28
1
1
[ "A010784", "A078255", "A154532", "A154566", "A357755" ]
null
Zhining Yang, Nov 26 2022
2025-03-23T20:53:21
oeisdata/seq/A357/A357755.seq
d44ca13eb7d6317a179aed4cd84d3048
A357756
a(n) is the least k > 0 such that A007953(n*k) equals A007953((n*k)^2), where A007953 is the sum of the digits.
[ "1", "1", "5", "3", "25", "2", "3", "27", "62", "1", "1", "5", "15", "27", "128", "3", "31", "17", "1", "1", "5", "9", "9", "2", "75", "4", "18", "7", "64", "5", "3", "16", "56", "3", "85", "17", "5", "27", "5", "9", "25", "9", "45", "13", "27", "1", "1", "27", "66", "54", "2", "9", "9", "18", "22", "1", "32", "15", "25", "135", "3", "18", "8", "3", "28", "9", "3", "43", "47", "72", "27", "8", "25", "126", "27" ]
[ "nonn", "base" ]
57
0
3
[ "A000010", "A007953", "A051628", "A058369", "A060284", "A132740", "A178505", "A357756" ]
null
Thomas Scheuerle, Oct 12 2022
2022-11-17T14:12:03
oeisdata/seq/A357/A357756.seq
329c10928dab4739604711713db94a5a
A357757
We draw n non-crossing straight line segments inside an n X n square between 2*n grid points on its perimeter in such a way that it is not possible to add more non-crossing line segments between the remaining perimeter grid points. a(n) is the number of distinct possibilities for each n without duplicates by rotation or reflection.
[ "1", "2", "18", "142", "1383", "14040", "148858", "1606567" ]
[ "nonn", "more" ]
42
1
2
null
null
Tamas Sandor Nagy, Nov 26 2022
2025-03-04T22:34:36
oeisdata/seq/A357/A357757.seq
1dcb11200795fd36f590d451ac6aa2dd
A357758
Numbers k such that in the binary expansion of k, the Hamming weight of each block differs by at most 1 from every other block of the same length.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "13", "14", "15", "16", "17", "18", "20", "21", "22", "23", "26", "27", "29", "30", "31", "32", "33", "34", "36", "37", "41", "42", "43", "45", "46", "47", "53", "54", "55", "59", "61", "62", "63", "64", "65", "66", "68", "72", "73", "74", "82", "84", "85", "86", "90", "91", "93", "94", "95", "106", "107", "109", "110", "111" ]
[ "nonn", "base" ]
10
1
3
[ "A005598", "A274008", "A357758", "A357759" ]
null
Rémy Sigrist, Oct 12 2022
2022-10-13T12:28:16
oeisdata/seq/A357/A357758.seq
3e0339769bfab6746e0bb0740791cdd4
A357759
Numbers k such that in the binary expansion of k, the Hamming weight of each block differs by at most 2 from every other block of the same length.
[ "0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70", "72", "73", "74", "75" ]
[ "nonn", "base" ]
18
1
3
[ "A274005", "A357758", "A357759" ]
null
Rémy Sigrist, Oct 12 2022
2024-10-09T18:31:16
oeisdata/seq/A357/A357759.seq
97584c2f1e534cae16d32b06e382a74f
A357760
a(n) is the number of different pairs of shortest grid paths joining two opposite corners in opposite order in an n X n X n grid with middle point on the paths as a common point.
[ "6", "1782", "163968", "145833750", "20373051636", "24849381916800", "4084135317043200", "5797029176271753750", "1041061545857195362500", "1615355981352350001296532", "306767275482371866616143872", "504734657532271646660879497344", "99610601729722879962014433236736", "170840233187582521064354430462720000" ]
[ "nonn" ]
54
1
1
null
null
Janaka Rodrigo, Oct 12 2022
2025-03-23T20:53:30
oeisdata/seq/A357/A357760.seq
b8abb70ef2c2f7700b5e425d02bbf6ce
A357761
a(n) = A227872(n) - A356018(n).
[ "1", "2", "0", "3", "0", "0", "2", "4", "-1", "0", "2", "0", "2", "4", "-2", "5", "0", "-2", "2", "0", "2", "4", "0", "0", "1", "4", "-2", "6", "0", "-4", "2", "6", "0", "0", "2", "-3", "2", "4", "0", "0", "2", "4", "0", "6", "-4", "0", "2", "0", "3", "2", "-2", "6", "0", "-4", "2", "8", "0", "0", "2", "-6", "2", "4", "0", "7", "0", "0", "2", "0", "0", "4", "0", "-4", "2", "4", "-2", "6", "2", "0", "2", "0", "-1", "4", "0" ]
[ "sign", "base", "easy" ]
11
1
2
[ "A000005", "A000069", "A000290", "A001969", "A027697", "A027699", "A046660", "A048272", "A106400", "A227872", "A230851", "A356018", "A357761", "A357762" ]
null
Amiram Eldar, Oct 12 2022
2022-10-14T09:23:42
oeisdata/seq/A357/A357761.seq
b60614ede6b0411e8864cf1f7e0b487e
A357762
Decimal expansion of -Sum_{k>=1} A106400(k)/k.
[ "1", "1", "9", "6", "2", "8", "3", "2", "6", "4", "3", "2", "5", "2", "5", "6", "4", "3", "7", "2", "2", "2", "2", "9", "1", "6", "3", "3", "2", "0", "0", "8", "1", "9", "1", "8", "1", "0", "1", "0", "4", "2", "6", "7", "4", "6", "4", "0", "1", "5", "9", "4", "3", "8", "1", "8", "9", "8", "7", "2", "3", "3", "3", "7", "3", "0", "7", "8", "3", "7", "5", "1", "6", "1", "0", "9", "1", "5", "8", "0", "8", "7", "7", "7", "9", "1", "1", "9", "6", "4", "5", "4", "6", "2", "1", "1", "0", "7", "4", "8", "9", "6", "3", "3", "3" ]
[ "nonn", "cons" ]
7
1
3
[ "A106400", "A215016", "A351404", "A357761", "A357762" ]
null
Amiram Eldar, Oct 12 2022
2022-10-12T11:39:44
oeisdata/seq/A357/A357762.seq
8e81b553b9b246172e1fd9d63d9024dd
A357763
Numbers m such that A357761(m) > A357761(k) for all k < m.
[ "1", "2", "4", "8", "16", "28", "56", "112", "224", "448", "728", "1456", "2912", "5824", "10192", "11648", "20384", "27664", "40768", "55328", "110656", "221312", "442624", "885248", "1263808", "1770496", "2527616", "3430336", "5055232", "6860672", "10110464", "13721344", "16155776", "20220928", "24012352", "32311552", "48024704" ]
[ "nonn", "base" ]
12
1
2
[ "A330289", "A355969", "A356020", "A357761", "A357763", "A357764" ]
null
Amiram Eldar, Oct 12 2022
2023-03-31T05:12:24
oeisdata/seq/A357/A357763.seq
da254412512000480844b2c56243699b
A357764
Numbers m such that A357761(m) < A357761(k) for all k < m.
[ "1", "3", "9", "15", "30", "60", "90", "180", "360", "540", "720", "1080", "2160", "4320", "6120", "8640", "12240", "18360", "24480", "36720", "73440", "146880", "257040", "293760", "514080", "587520", "807840", "1028160", "1615680", "1884960", "2056320", "2827440", "3231360", "3769920", "5654880", "7539840", "9424800", "11309760", "18849600" ]
[ "nonn", "base" ]
8
1
2
[ "A355969", "A356020", "A357761", "A357763", "A357764" ]
null
Amiram Eldar, Oct 12 2022
2022-10-13T05:49:42
oeisdata/seq/A357/A357764.seq
8055f213d8dc173fac4b7f2bcaeb584e
A357765
Smallest positive integer that can be represented as the sum of n of its (possibly equal) divisors in the maximum number of ways (=A002966(n)).
[ "1", "2", "12", "2520", "48348686786400", "10543141534556403817127800577537146514577188497111149855093902265479066128013109211427715400552367011213513440000" ]
[ "nice", "nonn" ]
9
1
2
[ "A002966", "A006585", "A181700", "A357765" ]
null
David A. Corneth and Max Alekseyev, Oct 12 2022
2022-10-13T12:52:03
oeisdata/seq/A357/A357765.seq
1699ea1aac4e27a0da76cf797c90feb9
A357766
Number of n X n tables where rows represent distinct permutations of { 1, 2, ..., n } and the column sums are equal.
[ "1", "2", "12", "2448", "6828480", "1386834134400", "20251525440458995200", "33182473074940946503237478400" ]
[ "hard", "more", "nonn" ]
6
1
2
[ "A356722", "A356723", "A356724", "A356725", "A357766", "A357767", "A357768" ]
null
Max Alekseyev, Oct 12 2022
2022-10-13T12:52:22
oeisdata/seq/A357/A357766.seq
0e5ff1ef92a4826cbb8bf662f9fad383
A357767
Number of n X n tables where rows represent distinct permutations of { 1, 2, ..., n } and the column sums are equal, up to permutation of rows.
[ "1", "1", "2", "102", "56904", "1926158520", "4018159809614880", "822978002850717919227120" ]
[ "hard", "more", "nonn" ]
6
1
3
[ "A356722", "A356723", "A356724", "A356725", "A357766", "A357767", "A357768" ]
null
Max Alekseyev, Oct 12 2022
2022-10-13T12:52:32
oeisdata/seq/A357/A357767.seq
99a6eaeaf739ae84ca5fd40e4750c8ed
A357768
Number of n X n tables where rows represent distinct permutations of { 1, 2, ..., n } and the column sums are equal, up to permutations of rows and columns.
[ "1", "1", "1", "9", "479", "2677443", "797253930582", "20411160794088064950" ]
[ "hard", "more", "nonn" ]
9
1
4
[ "A356722", "A356723", "A356724", "A356725", "A357766", "A357767", "A357768" ]
null
Max Alekseyev, Oct 13 2022
2022-10-18T06:23:36
oeisdata/seq/A357/A357768.seq
5ce1f06c7651ccd66c24f3af46850f0f
A357769
Positive numbers with decimal expansion d_1, ..., d_w that are divisible by d_1 + ... + d_k for k = 1..w.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "18", "20", "24", "30", "36", "40", "48", "50", "60", "70", "80", "90", "100", "102", "108", "110", "112", "114", "120", "126", "132", "140", "150", "156", "180", "190", "200", "204", "210", "216", "220", "224", "228", "230", "240", "252", "264", "270", "280", "300", "306", "312", "330", "336", "360", "396", "400" ]
[ "nonn", "base", "easy" ]
14
1
2
[ "A005349", "A034837", "A259433", "A328273", "A356350", "A357769" ]
null
Rémy Sigrist, Oct 12 2022
2022-10-17T07:06:41
oeisdata/seq/A357/A357769.seq
47b784019802ceffe9e71be3c8918d10
A357770
Number of 2n-step closed paths on quasi-regular rhombic (rhombille) lattice starting from a degree-3 node.
[ "1", "3", "30", "372", "5112", "74448", "1125408", "17461440", "276193152", "4433878272", "72022049280", "1181146106880", "19524892723200", "324921616773120", "5438136568504320", "91467357685235712", "1545090682931085312", "26199310348842762240", "445746455962332561408", "7606624602795641929728" ]
[ "nonn", "easy", "walk" ]
25
0
2
[ "A002893", "A002894", "A002898", "A357770", "A357771" ]
null
Dave R.M. Langers, Oct 12 2022
2025-03-23T20:51:46
oeisdata/seq/A357/A357770.seq
3cfbdfb4ca312e827cd85e712efbca38
A357771
Number of 2n-step closed paths on quasi-regular rhombic (rhombille) lattice starting from a degree-6 node.
[ "1", "6", "60", "744", "10224", "148896", "2250816", "34922880", "552386304", "8867756544", "144044098560", "2362292213760", "39049785446400", "649843233546240", "10876273137008640", "182934715370471424", "3090181365862170624", "52398620697685524480", "891492911924665122816", "15213249205591283859456", "260315328935885892747264" ]
[ "nonn", "easy", "walk" ]
33
0
2
[ "A002893", "A002894", "A002898", "A357770", "A357771" ]
null
Dave R.M. Langers, Oct 12 2022
2025-03-23T20:51:49
oeisdata/seq/A357/A357771.seq
cedadb0f05c10d9f095f3ff32e48b50d
A357772
Numbers with a sum of digits which is not 7-smooth.
[ "29", "38", "47", "49", "56", "58", "65", "67", "74", "76", "83", "85", "89", "92", "94", "98", "119", "128", "137", "139", "146", "148", "155", "157", "164", "166", "173", "175", "179", "182", "184", "188", "191", "193", "197", "199", "209", "218", "227", "229", "236", "238", "245", "247", "254", "256", "263" ]
[ "nonn", "easy", "base" ]
24
1
1
[ "A087144", "A357772" ]
null
Charles R Greathouse IV, Oct 13 2022
2022-10-13T11:36:54
oeisdata/seq/A357/A357772.seq
9001f498c82f7a57e5d9e93266f0f688
A357773
Odd numbers with two zeros in their binary expansion.
[ "9", "19", "21", "25", "39", "43", "45", "51", "53", "57", "79", "87", "91", "93", "103", "107", "109", "115", "117", "121", "159", "175", "183", "187", "189", "207", "215", "219", "221", "231", "235", "237", "243", "245", "249", "319", "351", "367", "375", "379", "381", "415", "431", "439", "443", "445", "463", "471", "475", "477", "487", "491", "493", "499", "501" ]
[ "nonn", "base", "easy" ]
65
1
1
[ "A000225", "A005408", "A018900", "A023416", "A048490", "A153894", "A190620", "A220236", "A353654", "A357773", "A357774" ]
null
Bernard Schott, Oct 12 2022
2024-12-18T09:27:29
oeisdata/seq/A357/A357773.seq
106b8a79b8d884e4e7d5f91aed414cf5
A357774
Binary expansions of odd numbers with two zeros in their binary expansion.
[ "1001", "10011", "10101", "11001", "100111", "101011", "101101", "110011", "110101", "111001", "1001111", "1010111", "1011011", "1011101", "1100111", "1101011", "1101101", "1110011", "1110101", "1111001", "10011111", "10101111", "10110111", "10111011", "10111101", "11001111", "11010111", "11011011", "11011101", "11100111", "11101011" ]
[ "nonn", "base" ]
34
1
1
[ "A000042", "A000217", "A007088", "A190619", "A267524", "A267705", "A357773", "A357774" ]
null
Bernard Schott, Oct 19 2022
2024-12-19T23:40:42
oeisdata/seq/A357/A357774.seq
6d581a0af59794377e6161211b7b13cc
A357775
Numbers k with the property that the symmetric representation of sigma(k) has seven parts.
[ "357", "399", "441", "483", "513", "567", "609", "621", "651", "729", "759", "777", "783", "837", "861", "891", "957", "999", "1023", "1053", "1089", "1107", "1131", "1161", "1209", "1221", "1269", "1287", "1323", "1353", "1419", "1431", "1443", "1521", "1551", "1595", "1599", "1677", "1705", "1749", "1815", "1833", "1887", "1947", "1989", "2013", "2035", "2067", "2091", "2145", "2193", "2223", "2255" ]
[ "nonn" ]
10
1
1
[ "A018411", "A174973", "A196020", "A235791", "A236104", "A237270", "A237271", "A237591", "A237593", "A238443", "A239663", "A239929", "A240062", "A266094", "A279102", "A280107", "A320066", "A320511", "A357775" ]
null
Omar E. Pol, Oct 12 2022
2022-10-23T23:38:19
oeisdata/seq/A357/A357775.seq
81fd1a6d08f3e8780ed0ff2593f6b7cb
A357776
Integer pairs that generate only odd prime sums (as described in comment).
[ "1", "2", "6", "11", "12", "17", "30", "41", "72", "101", "156", "546", "1481", "3917", "11886", "14627", "27737", "78696", "118901", "137436", "1676610", "12618762", "111018431", "574060031", "47357739281", "168920413410" ]
[ "nonn", "base", "more" ]
32
1
2
null
null
Bill McEachen, Oct 12 2022
2024-10-16T21:32:58
oeisdata/seq/A357/A357776.seq
52288fab018da90ad4ee92f515e6c1f4
A357777
a(1)=1, a(2)=2. Thereafter a(n+1) is the smallest k such that gcd(k, a(n)) > 1, and gcd(k, s(n)) = 1, where s(n) is the n-th partial sum.
[ "1", "2", "4", "6", "3", "9", "12", "8", "14", "7", "35", "5", "15", "10", "16", "20", "18", "21", "27", "24", "22", "11", "33", "30", "25", "55", "40", "26", "13", "39", "36", "28", "32", "34", "17", "51", "45", "57", "19", "133", "38", "44", "46", "23", "69", "42", "48", "50", "52", "54", "56", "49", "63", "60", "58", "29", "87", "66", "62", "31", "93", "72", "64", "68", "70", "65", "75", "78" ]
[ "nonn" ]
11
1
2
[ "A064413", "A357735", "A357777" ]
null
David James Sycamore, Oct 12 2022
2022-10-21T15:12:48
oeisdata/seq/A357/A357777.seq
17774ee50e558331b7e015a22fcff897
A357778
Maximum number of edges in a 5-degenerate graph with n vertices.
[ "0", "1", "3", "6", "10", "15", "20", "25", "30", "35", "40", "45", "50", "55", "60", "65", "70", "75", "80", "85", "90", "95", "100", "105", "110", "115", "120", "125", "130", "135", "140", "145", "150", "155", "160", "165", "170", "175", "180", "185", "190", "195", "200", "205", "210", "215", "220", "225", "230", "235" ]
[ "nonn" ]
17
1
3
[ "A004273", "A113127", "A296515", "A357778", "A357779" ]
null
Allan Bickle, Oct 13 2022
2024-02-18T02:09:10
oeisdata/seq/A357/A357778.seq
35b029cc7bb7600443c530ee7f33c90f
A357779
Maximum number of edges in a 6-degenerate graph with n vertices.
[ "0", "1", "3", "6", "10", "15", "21", "27", "33", "39", "45", "51", "57", "63", "69", "75", "81", "87", "93", "99", "105", "111", "117", "123", "129", "135", "141", "147", "153", "159", "165", "171", "177", "183", "189", "195", "201", "207", "213", "219", "225", "231", "237", "243", "249", "255", "261", "267", "273", "279" ]
[ "nonn" ]
16
1
3
[ "A004273", "A113127", "A296515", "A357778", "A357779" ]
null
Allan Bickle, Oct 13 2022
2024-02-18T12:17:37
oeisdata/seq/A357/A357779.seq
fb253c2068b5a3a35d67c73c08e3ceda
A357780
Primes p such that changing, in p, all 1's to 2's we get semiprimes and changing all 1's to 3's we get triprimes.
[ "61", "199", "313", "421", "619", "661", "1033", "1163", "1217", "1283", "1301", "1361", "1567", "1613", "1721", "1723", "1759", "1987", "2179", "2341", "2617", "3011", "3163", "3217", "4211", "4519", "4621", "5107", "7417", "8117", "8123", "8317", "8521", "9199", "9319", "9721", "9817", "10037", "10093", "10099", "10139", "10163", "10211", "10243", "10567", "10589", "10601", "10687", "10781", "10837", "10957" ]
[ "nonn", "base" ]
44
1
1
[ "A000040", "A001358", "A014612", "A357780" ]
null
Zak Seidov, Oct 14 2022
2023-12-17T11:13:12
oeisdata/seq/A357/A357780.seq
f7b913c3141cfb8b6b16bb50965b3e29
A357781
Semiprimes k such that k is congruent to 1 modulo k's index in the sequence of semiprimes.
[ "4", "82", "85", "106", "121", "133", "142", "166", "169", "217", "3067001", "3067006", "3067286", "3067411", "3067651", "3067691", "3067721", "3067751", "3067771", "3067781", "3067801", "3068071", "348933121", "348933127", "348933199", "348933223", "348933241", "348933259", "348933271", "348933427", "44690978221", "44690978543", "44690978669" ]
[ "nonn", "hard" ]
28
1
1
[ "A001358", "A106126", "A357781" ]
null
Lucas A. Brown, Oct 13 2022
2022-10-14T17:27:09
oeisdata/seq/A357/A357781.seq
5b8adf752be5df046e91591df630791c
A357782
a(n) = Sum_{k=0..floor(n/3)} 2^k * Stirling2(n,3*k).
[ "1", "0", "0", "2", "12", "50", "184", "686", "2996", "16642", "110328", "784190", "5645876", "40685762", "296458344", "2226254766", "17564381332", "147289101090", "1312394060536", "12305546886398", "119906479624084", "1202273551045474", "12341175064817576", "129582557972751918", "1394497073432776756" ]
[ "nonn" ]
24
0
4
[ "A143815", "A357782", "A357783", "A357784", "A357831" ]
null
Seiichi Manyama, Oct 13 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357782.seq
eff395961f15da2afce88ecbf6994a2d
A357783
a(n) = Sum_{k=0..floor((n-1)/3)} 2^k * Stirling2(n,3*k+1).
[ "0", "1", "1", "1", "3", "21", "131", "705", "3515", "17389", "91739", "547889", "3746227", "28241373", "224124083", "1821051233", "15023818091", "126366334125", "1094358852075", "9858890038513", "92983173940419", "918408372280477", "9454438841355395", "100728532687727329", "1103649166937235259" ]
[ "nonn" ]
22
0
5
[ "A143816", "A357782", "A357783", "A357784", "A357832" ]
null
Seiichi Manyama, Oct 13 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357783.seq
3c5357d57e25d1fc0964d81a356c985a
A357784
a(n) = Sum_{k=0..floor((n-2)/3)} 2^k * Stirling2(n,3*k+2).
[ "0", "0", "1", "3", "7", "17", "61", "343", "2231", "14301", "88561", "542011", "3397483", "22638993", "164336085", "1299899087", "10991061663", "97070035205", "881323166809", "8173386231395", "77489746906355", "754631383660729", "7590899551399869", "79174328607339767", "856889470005396071" ]
[ "nonn" ]
21
0
4
[ "A143817", "A357782", "A357783", "A357784", "A357833" ]
null
Seiichi Manyama, Oct 13 2022
2025-02-16T08:34:04
oeisdata/seq/A357/A357784.seq
399d94d9d3cc5850d8aeb0ffe1e76514
A357785
a(n) = coefficient of x^n, n >= 1, in A(x) such that: A(x)^2 = A( x^2/(1 - 4*x - 4*x^2) ) * sqrt(1 - 4*x - 4*x^2).
[ "1", "1", "4", "15", "65", "291", "1356", "6474", "31555", "156315", "784924", "3986534", "20444676", "105728100", "550735400", "2886924190", "15217019595", "80600822575", "428766983300", "2289637381800", "12268642450420", "65941128441080", "355396218177760", "1920215555772550", "10398415258863275" ]
[ "nonn" ]
18
1
3
[ "A357547", "A357785", "A357786" ]
null
Paul D. Hanna, Dec 03 2022
2022-12-04T08:34:20
oeisdata/seq/A357/A357785.seq
6fe34272fc265868555e47abcf383bec
A357786
a(n) = coefficient of x^n, n >= 1, in A(x) such that: A(x)^2 = A( x^2/(1 - 4*x - 8*x^2) ) * sqrt(1 - 4*x - 8*x^2).
[ "1", "1", "5", "20", "98", "483", "2499", "13182", "71030", "388484", "2152982", "12061840", "68212585", "388886050", "2232764700", "12898728750", "74923372563", "437303591874", "2563373794884", "15083551143318", "89060360731377", "527477003037984", "3132774700791126", "18652891302520806", "111314950683514698" ]
[ "nonn" ]
13
1
3
[ "A357548", "A357785", "A357786" ]
null
Paul D. Hanna, Dec 03 2022
2022-12-04T08:34:24
oeisdata/seq/A357/A357786.seq
96225b12887172ae65a06051164ebec9
A357787
a(n) = coefficient of x^n in A(x) such that C(x)^2 + S(x)^2 = 1 where: C(x) + i*S(x) = Sum_{n=-oo..+oo} i^n * (2*x)^(n^2) * A(x)^n.
[ "1", "2", "2", "8", "14", "32", "68", "0", "22", "-768", "-2020", "-9216", "-23156", "-45056", "-115320", "32768", "102118", "3391488", "8927532", "38993920", "100272484", "240910336", "602657464", "230686720", "307036796", "-14736687104", "-40340665064", "-204925304832", "-536096789800", "-1533403987968", "-3850562998512", "-4313489342464", "-8988517048442", "61275962867712" ]
[ "sign" ]
26
0
2
[ "A357787", "A357788", "A357789", "A357806" ]
null
Paul D. Hanna, Dec 04 2022
2022-12-06T13:15:13
oeisdata/seq/A357/A357787.seq
4ab16f9b86a3c9780308fb9aa5655418
A357788
a(n) = coefficient of x^(2*n) in C(x) defined by: C(x) + i*S(x) = Sum_{n=-oo..+oo} i^n * (2*x)^(n^2) * F(x)^n, where F(x) is the g.f. of A357787 such that C(x)^2 + S(x)^2 = 1.
[ "1", "0", "-32", "-256", "-2048", "-12288", "-32768", "131072", "3276800", "28311552", "125829120", "-285212672", "-11274289152", "-110326972416", "-511101108224", "2052994367488", "66383014526976", "707123415613440", "4088396548931584", "-1608585511436288", "-341992096703447040", "-4383726471663845376" ]
[ "sign" ]
14
0
3
[ "A357787", "A357788", "A357789", "A357806" ]
null
Paul D. Hanna, Dec 05 2022
2022-12-10T14:33:58
oeisdata/seq/A357/A357788.seq
e96e1f4e4a609b500a8ba2cb39bd2096
A357789
a(n) = coefficient of x^(2*n) in S(x) defined by: C(x) + i*S(x) = Sum_{n=-oo..+oo} i^n * (2*x)^(n^2) * F(x)^n, where F(x) is the g.f. of A357787 such that C(x)^2 + S(x)^2 = 1.
[ "8", "32", "128", "0", "-9216", "-94208", "-671744", "-3014656", "1245184", "171704320", "1756364800", "8338276352", "-26013073408", "-946201427968", "-10033714692096", "-56471303749632", "43465874341888", "4967278927937536", "61805829224923136", "423546310109429760", "713014908152709120", "-24149207336980840448" ]
[ "sign" ]
12
1
1
[ "A357787", "A357788", "A357789" ]
null
Paul D. Hanna, Dec 05 2022
2022-12-10T14:33:35
oeisdata/seq/A357/A357789.seq
7d10ebfe620d3615bc475fab0dacf279
A357790
a(n) = coefficient of x^n/n! in A(x) = Sum_{n>=0} x^n * cosh(sqrt(n)*x).
[ "1", "1", "2", "9", "48", "305", "2280", "19537", "188608", "2024577", "23911200", "308049401", "4298093184", "64555255921", "1038311141504", "17803434637185", "324148992092160", "6245040776838017", "126919440612205056", "2713418986517310313", "60871624993766717440", "1429679116231319002161" ]
[ "nonn" ]
16
0
3
null
null
Paul D. Hanna, Jan 01 2023
2023-01-04T12:39:31
oeisdata/seq/A357/A357790.seq
5491ad9aa80950a04899b9e6b357c70c
A357791
a(n) = coefficient of x^n in A(x) such that: x = Sum_{n=-oo..+oo} x^n * (1 - x^n * A(-x)^n)^n.
[ "1", "1", "2", "5", "21", "88", "377", "1654", "7424", "34000", "158274", "746525", "3559456", "17128250", "83078147", "405754479", "1993777057", "9849668910", "48892589632", "243739139810", "1219789105228", "6125813250402", "30862120708266", "155937956267432", "790019313067409", "4012282344217699", "20423575546661000" ]
[ "nonn" ]
8
0
3
[ "A357399", "A357791", "A359672" ]
null
Paul D. Hanna, Dec 24 2022
2023-01-11T10:22:54
oeisdata/seq/A357/A357791.seq
1f51e870ec71499bd757027e93eb1c81
A357792
a(n) = coefficient of x^n in A(x) = Sum_{n>=0} C(x)^n * (1 - C(x)^n)^n, where C(x) = x + C(x)^2 is a g.f. of the Catalan numbers (A000108).
[ "1", "1", "1", "3", "7", "20", "60", "189", "613", "2039", "6918", "23850", "83315", "294282", "1049279", "3771685", "13653313", "49730599", "182130129", "670274170", "2477514172", "9193599339", "34237330355", "127914531260", "479318575375", "1800971051420", "6783809423496", "25611913597250", "96903193235645", "367363376407250" ]
[ "nonn" ]
26
0
4
[ "A000108", "A357792", "A357793" ]
null
Paul D. Hanna, Dec 14 2022
2023-03-14T05:13:24
oeisdata/seq/A357/A357792.seq
bcf77c6239efdf931df3694cc625e510
A357793
a(n) = coefficient of x^n in A(x) = Sum_{n>=0} x^n*F(x)^n * (1 - x^n*F(x)^n)^n, where F(x) = 1 + x*F(x)^3 is a g.f. of A001764.
[ "1", "1", "1", "4", "14", "64", "314", "1633", "8826", "49107", "279349", "1617290", "9498099", "56445918", "338817460", "2051182532", "12509647159", "76785827812", "474000090118", "2940761033970", "18327028477625", "114677403429121", "720191795608082", "4537925593859911", "28679991910774479", "181761824439041725" ]
[ "nonn" ]
15
0
4
[ "A001764", "A357792", "A357793" ]
null
Paul D. Hanna, Dec 20 2022
2023-03-14T04:56:55
oeisdata/seq/A357/A357793.seq
7db30a683c4a8fa974265b74e4d4e007
A357794
a(n) = coefficient of x^n in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} n*(n+1)/2 * x^n * (1 - x^(n+1))^n * A(x)^(n+1).
[ "1", "3", "15", "114", "1086", "10824", "114382", "1252002", "14083275", "161810358", "1890774909", "22401092826", "268465408738", "3248818848876", "39643793276526", "487251937616006", "6026537732208078", "74954027622814455", "936840765257368687", "11761260253206563461", "148240496011414115676" ]
[ "nonn" ]
7
0
2
[ "A357158", "A357794", "A357795", "A357796" ]
null
Paul D. Hanna, Dec 22 2022
2022-12-24T11:17:07
oeisdata/seq/A357/A357794.seq
b252ac6d1ec346931e236468477266fe
A357795
a(n) = coefficient of x^n in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} n*(n+1)*(n+2)/3! * x^n * (1 - x^(n+2))^n * A(x)^(n+2).
[ "1", "4", "26", "300", "4134", "61696", "969660", "15837400", "266125823", "4571229248", "79904206064", "1416736880104", "25418030469904", "460600399886240", "8417980252615072", "154985730303047328", "2871904782258356719", "53519211809275995362", "1002383232008661189884", "18858606600633628740774" ]
[ "nonn" ]
7
0
2
[ "A357158", "A357794", "A357795", "A357796" ]
null
Paul D. Hanna, Dec 22 2022
2022-12-24T11:16:46
oeisdata/seq/A357/A357795.seq
fb311ce197cac87dd0e9745971be977c
A357796
a(n) = coefficient of x^n in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} n*(n+1)*(n+2)*(n+3)/4! * x^n * (1 - x^(n+3))^n * A(x)^(n+3).
[ "1", "5", "40", "635", "12095", "248245", "5381435", "121355095", "2817706420", "66909209195", "1617401484401", "39668321722180", "984661725380420", "24690230217076810", "624476169158179615", "15912858189842638180", "408139640637624168780", "10528308534373198776840", "272970775748658547320275" ]
[ "nonn" ]
7
0
2
[ "A357158", "A357794", "A357795", "A357796" ]
null
Paul D. Hanna, Dec 22 2022
2022-12-24T11:16:50
oeisdata/seq/A357/A357796.seq
9f002fc60280d680ba3b1f888cde5860
A357797
a(n) = coefficient of x^n in the power series A(x) such that: x = Sum_{n=-oo..+oo} (-1)^n * x^n * (2 + x^n)^n * A(x)^n.
[ "1", "1", "5", "18", "85", "374", "1659", "7774", "36876", "177494", "867424", "4285653", "21373782", "107475746", "544244911", "2773091748", "14207171278", "73140904609", "378184133959", "1963127909395", "10226682384980", "53446907352828", "280150058149086", "1472424136948438", "7758105323877698", "40970959715619200", "216830651728330127" ]
[ "nonn" ]
15
0
3
[ "A357797", "A357798", "A359720", "A359721", "A359723" ]
null
Paul D. Hanna, Dec 22 2022
2023-03-14T18:37:40
oeisdata/seq/A357/A357797.seq
d8ea6515df233f87d72ec9e42d52a640
A357798
a(n) = coefficient of x^n in the power series A(x) such that: 1 = Sum_{n=-oo..+oo} x^(n+1) * (2 - x^(n+1))^n * A(x)^n.
[ "1", "2", "6", "20", "78", "364", "1758", "9144", "48508", "264014", "1457624", "8158260", "46134878", "263312552", "1514534512", "8771202984", "51101608190", "299306977508", "1761377916048", "10409550718692", "61755225688926", "367639850029404", "2195551697108888", "13149811270786752", "78967249613057836", "475373797733460598" ]
[ "nonn" ]
7
0
2
[ "A357797", "A357798" ]
null
Paul D. Hanna, Dec 22 2022
2022-12-24T11:16:59
oeisdata/seq/A357/A357798.seq
ec498c8fa1133e67746d650351f8cbb7
A357799
a(n) = coefficient of x^n in A(x) such that: 1 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n+1)/2) * (A(x) + x^n)^(n+1).
[ "1", "1", "4", "10", "33", "105", "363", "1268", "4600", "16954", "63663", "242180", "932255", "3623239", "14200924", "56061965", "222728379", "889828825", "3572675122", "14408128581", "58338540673", "237067134533", "966522205819", "3952323714926", "16206324436147", "66621153183615", "274505283101713" ]
[ "nonn" ]
9
0
3
null
null
Paul D. Hanna, Dec 23 2022
2023-01-01T05:42:35
oeisdata/seq/A357/A357799.seq
b6d66f045877632e029012b8fdf3ad29
A357800
Coefficients T(n,k) of x^(4*n+1)*r^(4*k)/(4*n+1)! in power series S(x,r) = Integral C(x,r)^3 * D(x,r)^3 dx such that C(x,r)^4 - S(x,r)^4 = 1 and D(x,r)^4 - r^4*S(x,r)^4 = 1, as a symmetric triangle read by rows.
[ "1", "18", "18", "14364", "58968", "14364", "70203672", "671650056", "671650056", "70203672", "1192064637456", "20707300240704", "47530354598496", "20707300240704", "1192064637456", "52269828456672288", "1437626817559769760", "5941554215913771840", "5941554215913771840", "1437626817559769760", "52269828456672288", "4930307288899134335424", "197041019249105562351744", "1283341580573615116868160", "2308585363008068715943680" ]
[ "nonn", "tabl" ]
8
0
2
[ "A153301", "A357540", "A357800", "A357801", "A357802", "A357804" ]
null
Paul D. Hanna, Oct 14 2022
2022-10-15T10:37:20
oeisdata/seq/A357/A357800.seq
4ac9de9815b5a5456c2cc5b6b57dbb8e