A356576 Expansion of e.g.f. ( Product_{k>0} (1+x^k)^(1/k!) )^x.
1, 0, 2, 0, 24, -55, 630, -2723, 30968, -294327, 3047320, -30255379, 387690732, -5565964391, 77090414492, -1114263777885, 18473122449616, -331776991760303, 6106973926830192, -112710455017397639, 2233663985151902860, -50049383051597936559
Offset: 0
Keywords
Programs
-
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(1/k!))^x)) -
PARI
a352013(n) = (n-1)!*sumdiv(n, d, (-1)^(n/d+1)/(d-1)!); a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*a352013(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
Formula
a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k * A352013(k-1) * binomial(n-1,k-1) * a(n-k).