A356524 Expansion of e.g.f. Product_{k>0} 1/(1 - k * x^k)^(1/k!).

1, 1, 4, 15, 100, 565, 5946, 46039, 605256, 6646329, 103614490, 1320840631, 27185208876, 401901829069, 9042437722878, 168984439301175, 4257225193170256, 85582303577644465, 2593970612953642386, 57441717948059605927, 1862688382990615542900

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A354849(k) * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k*x^k)^(1/k!))))
(PARI) a354849(n) = (n-1)!*sumdiv(n, d, d^(n/d)/(d-1)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354849(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A006906, A209902, A294462, A354849, A356487.

Sequence in context: A109365 A352415 A079128 * A289489 A221095 A339287

Adjacent sequences: A356521 A356522 A356523 * A356525 A356526 A356527

Keyword

nonn

Author

Seiichi Manyama, Aug 10 2022

Status

approved