A355064 Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k)^(1/k) )^x.

1, 0, 2, 6, 28, 210, 1248, 13020, 102128, 1248912, 13457880, 176726880, 2362784928, 36609693120, 551337892896, 9588702417840, 171779733546240, 3230529997766400, 64714946343904512, 1371420774325866240, 29953522454811096960, 698447624328756610560

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..445

Formula

a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k! * sigma_0(k-1)/(k-1) * binomial(n-1,k-1) * a(n-k).

Mathematica

a[0] := a[0] = 1; a[1] := a[1] = 0;
a[n_] := a[n] = Sum[Factorial[k]*DivisorSigma[0, k - 1]/(k - 1)*Binomial[n - 1, k - 1]* a[n - k], {k, 2, n}];
Table[a[n], {n, 0, 50}] (* Sidney Cadot, Jan 05 2023 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^(1/k))^x))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j!*sigma(j-1, 0)/(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A354623, A356554.

Cf. A000005, A066166, A356336, A356564.

Sequence in context: A272662 A125812 A093657 * A305627 A006117 A118025

Adjacent sequences: A355061 A355062 A355063 * A355065 A355066 A355067

Keyword

nonn

Author

Seiichi Manyama, Aug 12 2022

Status

approved