A356495 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, 10, 191, 7287, 424292, 37434683, 4512452023, 726390985036, 149098938941283, 38187088904721655, 11903871288193251930, 4442392007373264794677, 1953788894138983864638457, 1000334575509506861927067378, 589712001176601700420819946615

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A354892(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) a354892(n) = n!*sumdiv(n, d, d^n/(n/d)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354892(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A209903, A346055, A356494.

Cf. A000110, A354892.

Sequence in context: A144772 A045756 A072387 * A244385 A134633 A006436

Adjacent sequences: A356492 A356493 A356494 * A356496 A356497 A356498

Keyword

nonn

Author

Seiichi Manyama, Aug 09 2022

Status

approved