A384414 Expansion of Product_{k>=1} 1/(1 - k^4 * x)^((1/30) * (2/3)^k).

1, 73, 2271421, 664978095445, 805854449283423655, 2773445081734579264589407, 21807207369084946567603587345091, 339838389273170021807379637478064625867, 9495034758014772381226851471008240873743234210, 441461703234194795490537796224906335240071042475017490

Offset: 0

Author

Seiichi Manyama, May 28 2025

Keywords

• nonn

Crossrefs

Cf. A004123, A384412.

Programs

PARI

b(n) = sum(k=0, n, 2^k*k!*stirling(n, k, 2));
my(N=10, x='x+O('x^N)); Vec(exp(sum(k=1, N, b(4*k)*x^k/k)/10))

Formula

G.f.: exp((1/10) * Sum_{k>=1} b(4*k) * x^k/k), where b(n) = Sum_{k=0..n} 2^k * k! * Stirling2(n,k).