A384357 Expansion of Product_{k>=1} 1/(1 - k*(k+1)*(k+2)/6 * x)^((1/54) * (2/3)^k).

1, 1, 153, 128793, 319155321, 1744213657689, 17803590830142393, 304609764628470426969, 8095576593110601916260369, 315845539893724747798646514673, 17317064152543324914717101316522961, 1288754843591816442932799782872809777393, 126555732798742295186573610437899751882638209

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(3, k)*x^k/k)/8))

Formula

G.f.: exp((1/8) * Sum_{k>=1} A384362(3,k) * x^k/k).