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

Author

Seiichi Manyama, May 28 2025

Keywords

• nonn

Crossrefs

Cf. A004123, A050351, A247082, A384414.

Programs

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).