A356561 - OEIS

%I #10 Aug 12 2022 09:21:13

%S 1,1,4,18,204,1260,37440,299880,11002320,204860880,6618628800,

%T 92924647200,8181137764800,124123075876800,7211104918617600,

%U 288085376346768000,14964000305173920000,340302035937191328000,42619767305209750656000

%N Expansion of e.g.f. Product_{k>0} 1/(1 - k^3 * x^k)^(1/k^3).

%F a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A308689(k) * a(n-k)/(n-k)!.

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k^3*x^k)^(1/k^3))))

%o (PARI) a308689(n) = sumdiv(n, d, d^(3*n/d-2));

%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a308689(j)*v[i-j+1]/(i-j)!)); v;

%Y Cf. A294462, A294469, A356530, A356560.

%Y Cf. A265837, A308689.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 12 2022