A356560 Expansion of e.g.f. Product_{k>0} 1/(1 - k^2 * x^k)^(1/k^2).

1, 1, 4, 18, 156, 1020, 16560, 143640, 2898000, 43016400, 926856000, 13749674400, 524416939200, 8626888670400, 284030505158400, 7950850859952000, 284397434953632000, 6752059834744224000, 357295791069689472000, 9098085523917918528000

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A308688(k) * a(n-k)/(n-k)!.

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k^2*x^k)^(1/k^2))))
(PARI) a308688(n) = sumdiv(n, d, d^(2*n/d-1));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a308688(j)*v[i-j+1]/(i-j)!)); v;

Crossrefs

Cf. A294462, A294469, A356530, A356561.

Cf. A077335, A308688.

Sequence in context: A054759 A286630 A330467 * A356530 A222766 A302827

Adjacent sequences: A356557 A356558 A356559 * A356561 A356562 A356563

Keyword

nonn

Author

Seiichi Manyama, Aug 12 2022

Status

approved