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A356566
Expansion of e.g.f. ( Product_{k>0} (1+x^k)^k )^x.
3
1, 0, 2, 9, 92, 510, 7074, 68040, 1002224, 12529944, 228706920, 3565888920, 71035245192, 1348127454960, 30270949077264, 661700017709640, 16516072112482560, 408336559236083520, 11204399270843020224, 309489391954850336640, 9258803420755891835520
OFFSET
0,3
FORMULA
a(0) = 1, a(1) = 0; a(n) = Sum_{k=2..n} k! * A078306(k-1)/(k-1) * 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)^k)^x))
(PARI) a078306(n) = sumdiv(n, d, (-1)^(n/d+1)*d^2);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j!*a078306(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