A352841 Expansion of e.g.f. 1/(1 - Sum_{k>=1} sigma_k(k) * x^k/k!).
1, 1, 7, 64, 851, 13906, 277972, 6466650, 172651643, 5186830537, 173327806752, 6373233407498, 255743444526584, 11119651415719744, 520752884139087852, 26132341317365562754, 1398900109763305183707, 79569524691656775423766
Offset: 0
Keywords
Programs
-
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, sigma(k, k)*x^k/k!)))) -
PARI
a(n) = if(n==0, 1, sum(k=1, n, sigma(k, k)*binomial(n, k)*a(n-k)));
Formula
a(0) = 1; a(n) = Sum_{k=1..n} sigma_k(k) * binomial(n,k) * a(n-k).