A377963 Expansion of e.g.f. (1+x) * exp(x*(1+x)^2).

1, 2, 7, 34, 173, 1066, 7147, 51962, 412729, 3478258, 31220111, 296409202, 2953487077, 30870965594, 336796018483, 3824230997386, 45114077004017, 551338045973602, 6968344940992279, 90931562913957698, 1222939213021853341, 16929504703420184842, 240909000856701880187

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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.

Prog

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

Crossrefs

Cf. A018191, A377964.

Cf. A361278, A377965.

Sequence in context: A353343 A376055 A023053 * A058915 A273030 A020054

Adjacent sequences: A377960 A377961 A377962 * A377964 A377965 A377966

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 12 2024

Status

approved