A377966
Expansion of e.g.f. (1+x)^2 * exp(x*(1+x)^3).
Original entry on oeis.org
1, 3, 13, 85, 621, 5131, 48553, 500613, 5590105, 67453651, 868300581, 11854859413, 171122864773, 2598083998875, 41331779697601, 687151457132101, 11904595227392433, 214378528158055843, 4004773210169606845, 77459628036613435221, 1548502062887370346141
Offset: 0
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a(n, s=2, t=3) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);
A377963
Expansion of e.g.f. (1+x) * exp(x*(1+x)^2).
Original entry on oeis.org
1, 2, 7, 34, 173, 1066, 7147, 51962, 412729, 3478258, 31220111, 296409202, 2953487077, 30870965594, 336796018483, 3824230997386, 45114077004017, 551338045973602, 6968344940992279, 90931562913957698, 1222939213021853341, 16929504703420184842, 240909000856701880187
Offset: 0
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a(n, s=1, t=2) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);
A377967
Expansion of e.g.f. (1+x)^3 * exp(x*(1+x)^3).
Original entry on oeis.org
1, 4, 19, 124, 961, 8236, 79339, 840484, 9595009, 117764596, 1542837091, 21406165804, 313381177729, 4822681240924, 77704955681851, 1307128152596116, 22899018541506049, 416756647023727204, 7863586717014612019, 153550319029835965276, 3097694623619639050561
Offset: 0
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With[{nn=20},CoefficientList[Series[(1+x)^3 Exp[x*(1+x)^3],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 28 2025 *)
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a(n, s=3, t=3) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);
A378016
E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x)^2 * A(x) ).
Original entry on oeis.org
1, 2, 11, 115, 1617, 30241, 701923, 19517975, 633387905, 23513238865, 983268873891, 45750603668815, 2344878934878769, 131285573039583977, 7973124098907905603, 522086636316439329511, 36669284618683152764289, 2750044026126526125774625, 219342360538110975815216323
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)*exp(-lambertw(-x*(1+x)^3))))
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a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(3*k+1, n-k)/k!);
Showing 1-4 of 4 results.