cp's OEIS Frontend

A326865 G.f.: Product_{k>=1} (1 + x^k/k^3) = Sum_{n>=0} a(n)*x^n/n!^3.

%I A326865 #11 Jul 27 2023 16:32:26
%S A326865 1,1,1,35,728,48824,7170984,1418111064,479963197440,235727037775872,
%T A326865 170423013422592000,163854260184125952000,214343327259234349056000,
%U A326865 360795240553638133592064000,778954481701636984110452736000,2095759092922096320907078496256000
%N A326865 G.f.: Product_{k>=1} (1 + x^k/k^3) = Sum_{n>=0} a(n)*x^n/n!^3.
%H A326865 Alois P. Heinz, <a href="/A326865/b326865.txt">Table of n, a(n) for n = 0..182</a>
%F A326865 a(n) ~ c * (n-1)!^3, where c = A073017 = Product_{k>=1} (1 + 1/k^3) = cosh(sqrt(3)*Pi/2)/Pi = 2.428189792098870328736...
%p A326865 b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,
%p A326865       b(n, i-1)+b(n-i, min(n-i, i-1))*((i-1)!*binomial(n, i))^3))
%p A326865     end:
%p A326865 a:= n-> b(n$2):
%p A326865 seq(a(n), n=0..20);  # _Alois P. Heinz_, Jul 27 2023
%t A326865 nmax = 20; CoefficientList[Series[Product[(1+x^k/k^3), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!^3
%Y A326865 Cf. A007838, A249593, A326864.
%K A326865 nonn
%O A326865 0,4
%A A326865 _Vaclav Kotesovec_, Jul 27 2019