A377967 -id:A377967 - cp's OEIS frontend

A377964 Expansion of e.g.f. (1+x) * exp(x*(1+x)^3).

1, 2, 9, 58, 389, 3186, 29437, 294554, 3233673, 38350594, 484794641, 6522118362, 92857444429, 1390937221298, 21858658599429, 359271578140666, 6156249977141777, 109722278546645634, 2029772196329985433, 38893956306343711994, 770622936760496106261, 15763542538016019828082

Offset: 0

Seiichi Manyama, Nov 12 2024

Cf. A018191, A377963.

Cf. A361279, A377966, A377967.

a(n, s=1, t=3) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);

a(n) = n! * Sum_{k=0..n} binomial(3*k+1,n-k) / k!.

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

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!.

cp's OEIS Frontend

A377964 Expansion of e.g.f. (1+x) * exp(x*(1+x)^3).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula