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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 12 2022
STATUS
approved