A384359 Expansion of Product_{k>=1} 1/(1 - k*(k+1)/2 * x)^((1/48) * (3/4)^k).

1, 1, 37, 4453, 1126375, 489185863, 324848377243, 306044183298331, 388203452145317314, 637855747987693348770, 1317841032827800659419754, 3343784211346797764798294634, 10221662989279986155378379955158, 37051850653048390530321630384383382, 157140052593846256021318451838028238910

Offset: 0

Author

Seiichi Manyama, May 27 2025

Keywords

• nonn

Crossrefs

Cf. A384364.

Programs

PARI

a384364(n, k) = sum(i=0, k*n, 3^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, a384364(2, k)*x^k/k)/9))

Formula

G.f.: exp((1/9) * Sum_{k>=1} A384364(2,k) * x^k/k).