A384412 Expansion of Product_{k>=1} 1/(1 - k^2 * x)^((1/30) * (2/3)^k).
1, 1, 37, 4477, 1139503, 498101431, 332955009307, 315774077663395, 403232260150593946, 667010006578379121074, 1387375789650073950228650, 3544016332332206162590402778, 10907098996548018595779254922854, 39804369748279182675138824291484662, 169958609977149735126105997027662792638
Offset: 0
Keywords
Programs
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PARI
b(n) = sum(k=0, n, 2^k*k!*stirling(n, k, 2)); my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, b(2*k)*x^k/k)/10))
Formula
G.f.: exp((1/10) * Sum_{k>=1} b(2*k) * x^k/k), where b(n) = Sum_{k=0..n} 2^k * k! * Stirling2(n,k).