A356487 Expansion of e.g.f. Product_{k>0} 1/(1 - (k * x)^k)^(1/k!).

1, 1, 6, 45, 580, 7105, 170076, 2654575, 116426528, 2386183761, 209503380160, 3455683548691, 969334978024920, 15164681616944353, 6510178188269825720, 223847763757748796975, 81261936394687862700256, 1581790511799886415713825

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A356486(k) * binomial(n-1,k-1) * a(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) a356486(n) = (n-1)!*sumdiv(n, d, d^n/(d-1)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356486(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A023882, A209902, A356486.

Sequence in context: A078865 A160492 A318017 * A322089 A273091 A086721

Adjacent sequences: A356484 A356485 A356486 * A356488 A356489 A356490

Keyword

nonn

Author

Seiichi Manyama, Aug 09 2022

Status

approved