A384352 Expansion of Product_{k>=1} 1/(1 - k*(k+1)*(k+2)/6 * x)^((1/2)^(k+3)).

1, 1, 32, 5392, 2676188, 2930633692, 5993325199448, 20540879727692152, 109337218761743017718, 854254522610491562826582, 9378640254148405369808277352, 139752461092050444767050922501096, 2747716352285121538660626991038190636, 69628008338488529846443753577404293410060

Offset: 0

Author

Seiichi Manyama, May 27 2025

Keywords

• nonn

Crossrefs

Cf. A084784, A384351, A384353.

Cf. A062208, A262809.

Programs

PARI

a262809(n, k) = sum(i=0, k*n, 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, a262809(3, k)*x^k/k)))

Formula

G.f.: exp(Sum_{k>=1} A062208(k) * x^k/k).