A356494 Expansion of e.g.f. Product_{k>0} B(k * x^k) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers.

1, 1, 6, 35, 327, 2892, 37943, 459895, 7330172, 116054835, 2168292295, 41072348550, 898738816957, 19782331776937, 487091519709590, 12305361661242275, 337777113607935587, 9528258228302443724, 289373132780801591323, 9016757353084706862647

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A354843(k) * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(exp(k*x^k)-1))))
(PARI) a354843(n) = n!*sumdiv(n, d, (n/d)^d/d!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354843(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A209903, A346055, A356495.

Cf. A000110, A354843, A356460.

Sequence in context: A356460 A261073 A261080 * A291595 A268139 A361241

Adjacent sequences: A356491 A356492 A356493 * A356495 A356496 A356497

Keyword

nonn

Author

Seiichi Manyama, Aug 09 2022

Status

approved