A384408 - OEIS

%I #11 May 29 2025 07:57:35

%S 1,13,2426,2393226,7056543721,46153703519501,564874416706639304,

%T 11596724623199364432312,369937054535706501459633546,

%U 17326810763609633232550088712162,1140582994940898154002780391375267884,101920298764725526200442366857326292990348

%N Expansion of Product_{k>=1} 1/(1 - k^3 * x)^((1/2)^(k+1)).

%F G.f.: exp(Sum_{k>=1} A000670(3*k) * x^k/k).

%F 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

%o (PARI) a000670(n) = sum(k=0, n, k!*stirling(n, k, 2));

%o my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, a000670(3*k)*x^k/k)))

%Y Cf. A084784, A384410.

%Y Cf. A249941.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 28 2025