A371184 Expansion of e.g.f. (1 + x^3 + x^4)^x.

1, 0, 0, 0, 24, 120, 0, -2520, -20160, 181440, 3024000, 19958400, -159667200, -5708102400, -47221574400, 326918592000, 20748433305600, 296406190080000, -533531142144000, -126713646259200000, -3007337204551680000, -14688645874366464000, 1183099972392898560000

Offset

0,5

Links

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

Formula

a(n) = n! * Sum_{j=0..floor(n/3)} Sum_{k=0..j} binomial(j,n-3*j-k) * Stirling1(j,k)/j!.

Prog

(PARI) a(n) = n!*sum(j=0, n\3, sum(k=0, j, binomial(j, n-3*j-k)*stirling(j, k, 1)/j!));

Crossrefs

Cf. A371160.

Sequence in context: A211580 A211594 A211465 * A371160 A371200 A293893

Adjacent sequences: A371181 A371182 A371183 * A371185 A371186 A371187

Keyword

sign

Author

Seiichi Manyama, Mar 14 2024

Status

approved