A356542 Expansion of e.g.f. Product_{k>0} 1/(1 - k! * x^k)^(1/k!).

1, 1, 4, 18, 132, 900, 11160, 100800, 1809360, 25053840, 608428800, 8610386400, 469291838400, 7110609105600, 404607162960000, 13958116204032000, 821937470818464000, 17420311428103584000, 2860701872247483264000, 60029296274562398784000

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A356541(k) * a(n-k)/(n-k)!.

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k!*x^k)^(1/k!))))
(PARI) a356541(n) = sumdiv(n, d, d*d!^(n/d-1));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a356541(j)*v[i-j+1]/(i-j)!)); v;

Crossrefs

Cf. A209902, A356524, A356541.

Sequence in context: A034517 A294462 A194559 * A371038 A065857 A214647

Adjacent sequences: A356539 A356540 A356541 * A356543 A356544 A356545

Keyword

nonn

Author

Seiichi Manyama, Aug 11 2022

Status

approved