OFFSET
0,3
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} A354509(k) * binomial(n-1,k-1) * a(n-k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(1/k!))^exp(x)))
(PARI) a354509(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(d+1)/(d*(k/d)!))/(n-k)!);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354509(j)*binomial(i-1, j-1)*v[i-j+1])); v;
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 15 2022
STATUS
approved