A356566 Expansion of e.g.f. ( Product_{k>0} (1+x^k)^k )^x.

1, 0, 2, 9, 92, 510, 7074, 68040, 1002224, 12529944, 228706920, 3565888920, 71035245192, 1348127454960, 30270949077264, 661700017709640, 16516072112482560, 408336559236083520, 11204399270843020224, 309489391954850336640, 9258803420755891835520

Offset

0,3

Links

Table of n, a(n) for n=0..20.

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

Cf. A356564, A356565.

Cf. A007113, A078306, A356394.

Sequence in context: A368840 A224323 A240650 * A365363 A011804 A292467

Adjacent sequences: A356563 A356564 A356565 * A356567 A356568 A356569

Keyword

nonn

Author

Seiichi Manyama, Aug 12 2022

Status

approved