A357192 a(n) = n! * Sum_{k=0..floor(n/3)} k^n/k!.

1, 0, 0, 6, 24, 120, 23760, 327600, 5201280, 1283688000, 37574409600, 1219438281600, 378254710310400, 19092171351052800, 1045282110435763200, 394211859168070944000, 30499777423295212032000, 2523689643597315088896000, 1125362204955051396299366400

Offset

0,4

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: Sum_{k>=0} (k * x)^(3 * k) / (k! * (1 - k * x)).

Prog

(PARI) a(n) = n!*sum(k=0, n\3, k^n/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*x)^(3*k)/(k!*(1-k*x)))))

Crossrefs

Cf. A256016, A357191.

Cf. A352982, A357194.

Sequence in context: A376516 A376495 A376475 * A357194 A188232 A274072

Adjacent sequences: A357189 A357190 A357191 * A357193 A357194 A357195

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2022

Status

approved