OFFSET
0,3
FORMULA
a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k! * A000593(k-1)/(k-1) * binomial(n-1,k-1) * a(n-k).
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[(1 + x^k)^x, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Aug 17 2022 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, 1+x^k)^x))
(PARI) a000593(n) = sumdiv(n, d, (-1)^(n/d+1)*d);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j!*a000593(j-1)/(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 12 2022
STATUS
approved