A356892 E.g.f. satisfies log(A(x)) = x^3 * (exp(x * A(x)) - 1) * A(x).

1, 0, 0, 0, 24, 60, 120, 210, 101136, 1089144, 7409520, 39917790, 4097460840, 100410712116, 1474154203704, 16356956618730, 786764261166240, 30867868254267120, 778327514455987296, 14658714575197061814, 522720977799308061240, 25075479032600008569900

Offset

0,5

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (n-2*k+1)^(k-1) * Stirling2(n-3*k,k)/(n-3*k)!.

Mathematica

m = 22; (* number of terms *)
A[_] = 0;
Do[A[x_] = Exp[x^3*(Exp[x*A[x]] - 1)*A[x]] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m-1]! (* Jean-François Alcover, Sep 12 2022 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\4, (n-2*k+1)^(k-1)*stirling(n-3*k, k, 2)/(n-3*k)!);

Crossrefs

Cf. A349557, A356785, A355508.

Cf. A356963.

Sequence in context: A366751 A358014 A356950 * A376293 A370990 A182464

Adjacent sequences: A356889 A356890 A356891 * A356893 A356894 A356895

Keyword

nonn

Author

Seiichi Manyama, Sep 07 2022

Status

approved