A357032 E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^3 / 6.

1, 0, 0, 1, 6, 25, 160, 1981, 24906, 295625, 4044900, 68136541, 1260048086, 24330807865, 508029259920, 11686882860381, 289532464998146, 7588430921962825, 210991834698749020, 6244230552027963901, 195584639712483465486, 6442981074293371848185

Offset

0,5

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (3*k)! * (n+1)^(k-1) * Stirling2(n,3*k)/(6^k * k!).

Prog

(PARI) a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*stirling(n, 3*k, 2)/(6^k*k!));

Crossrefs

Cf. A030019, A357031.

Cf. A327504, A357025.

Sequence in context: A009464 A042529 A323132 * A183249 A199008 A356909

Adjacent sequences: A357029 A357030 A357031 * A357033 A357034 A357035

Keyword

nonn

Author

Seiichi Manyama, Sep 09 2022

Status

approved