A384408 Expansion of Product_{k>=1} 1/(1 - k^3 * x)^((1/2)^(k+1)).
1, 13, 2426, 2393226, 7056543721, 46153703519501, 564874416706639304, 11596724623199364432312, 369937054535706501459633546, 17326810763609633232550088712162, 1140582994940898154002780391375267884, 101920298764725526200442366857326292990348
Offset: 0
Keywords
Programs
-
PARI
a000670(n) = sum(k=0, n, k!*stirling(n, k, 2)); my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, a000670(3*k)*x^k/k)))
Formula
G.f.: exp(Sum_{k>=1} A000670(3*k) * x^k/k).
a(n) ~ sqrt(Pi) * 3^(3*n + 1/2) * n^(3*n - 1/2) / (sqrt(2) * exp(3*n) * log(2)^(3*n+1)). - Vaclav Kotesovec, May 29 2025