A384356 Expansion of Product_{k>=1} 1/(1 - k*(k+1)/2 * x)^((1/18) * (2/3)^k).

1, 1, 19, 1147, 145606, 31784062, 10617130378, 5033441934298, 3213448742033479, 2657684269018334807, 2763967539211567981613, 3530274805575983022456005, 5432490565296371673408076892, 9912854399723224290769677025316, 21163615551469069985356131546443588

Offset: 0

Author

Seiichi Manyama, May 27 2025

Keywords

• nonn

Crossrefs

Cf. A384362.

Programs

PARI

a384362(n, k) = sum(i=0, k*n, 2^i*sum(j=0, i, (-1)^j*binomial(i, j)*binomial(i-j, n)^k));
my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, a384362(2, k)*x^k/k)/4))

Formula

G.f.: exp((1/4) * Sum_{k>=1} A384362(2,k) * x^k/k).