A377965 -id:A377965 - cp's OEIS frontend

A377966 Expansion of e.g.f. (1+x)^2 * exp(x*(1+x)^3).

1, 3, 13, 85, 621, 5131, 48553, 500613, 5590105, 67453651, 868300581, 11854859413, 171122864773, 2598083998875, 41331779697601, 687151457132101, 11904595227392433, 214378528158055843, 4004773210169606845, 77459628036613435221, 1548502062887370346141

Offset: 0

Seiichi Manyama, Nov 12 2024

Cf. A377954, A377965.

Cf. A361279, A377964, A377967.

a(n, s=2, t=3) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);

a(n) = n! * Sum_{k=0..n} binomial(3*k+2,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

Seiichi Manyama, Nov 12 2024

Cf. A018191, A377964.

Cf. A361278, A377965.

a(n, s=1, t=2) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);

a(n) = n! * Sum_{k=0..n} binomial(2*k+1,n-k) / k!.

a(n) = a(n-1) + (4*n-3)*a(n-2) + 3*(n-2)*n*a(n-3) for n > 2.

cp's OEIS Frontend

A377966 Expansion of e.g.f. (1+x)^2 * exp(x*(1+x)^3).

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