A370321 Expansion of e.g.f. (1 + x + x^2)^(x^2).

1, 0, 0, 6, 12, -80, 540, 3528, -35280, 82080, 3346560, -33153120, -82257120, 6269253120, -54446648256, -587596363200, 20753512416000, -140977071406080, -3956109141496320, 111209937855367680, -474928112845670400, -36237656611756615680, 911155391189543808000

Offset

0,4

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A371157.

Sequence in context: A061520 A305058 A220232 * A196253 A338563 A345271

Adjacent sequences: A370318 A370319 A370320 * A370322 A370323 A370324

Keyword

sign

Author

Seiichi Manyama, Mar 14 2024

Status

approved