A356785 E.g.f. satisfies log(A(x)) = x * (exp(x*A(x)) - 1) * A(x).

1, 0, 2, 3, 64, 365, 7356, 85687, 1920752, 34821369, 905128300, 22172123171, 672107454888, 20552960420005, 721088019634724, 26257726364294895, 1053711696230404576, 44336326818388565105, 2010106841636689325532, 95747319823049127621019

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

Mathematica

nmax = 19; A[_] = 1;
Do[A[x_] = Exp[x*(Exp[x*A[x]]-1)*A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 04 2024 *)

Prog

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

Crossrefs

Cf. A349560, A356788, A356789.

Cf. A184949, A349557, A355843.

Sequence in context: A037426 A004854 A356797 * A015169 A041953 A099080

Adjacent sequences: A356782 A356783 A356784 * A356786 A356787 A356788

Keyword

nonn

Author

Seiichi Manyama, Aug 27 2022

Status

approved