A371175 Expansion of e.g.f. (1 + x^2 + x^3)^x.

1, 0, 0, 6, 24, -60, -360, 4200, 40320, -211680, -4384800, 11309760, 738460800, 1816214400, -148445256960, -1475025552000, 32459383756800, 764727970406400, -5456626240665600, -382783823399577600, -1390652097778944000, 189934744994362368000

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n! * Sum_{j=0..floor(n/2)} Sum_{k=0..j} binomial(j,n-2*j-k) * Stirling1(j,k)/j!.

Prog

(PARI) a(n) = n!*sum(j=0, n\2, sum(k=0, j, binomial(j, n-2*j-k)*stirling(j, k, 1)/j!));

Crossrefs

Cf. A371159.

Sequence in context: A265393 A292908 A293017 * A292889 A366546 A272951

Adjacent sequences: A371172 A371173 A371174 * A371176 A371177 A371178

Keyword

sign

Author

Seiichi Manyama, Mar 14 2024

Status

approved