A384353 Expansion of Product_{k>=1} 1/(1 - k*(k+1)*(k+2)*(k+3)/24 * x)^((1/2)^(k+4)).

1, 1, 161, 233201, 1388333781, 23407417517205, 900363695229160325, 68584682130559722233525, 9362104205577409136806214275, 2125938144923623062958782871506275, 758178276483321320080629434392636915075, 405630344408921348237973282862682052175313075

Offset: 0

Author

Seiichi Manyama, May 27 2025

Keywords

• nonn

Crossrefs

Cf. A084784, A384351, A384352.

Cf. A062205, 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(4, k)*x^k/k)))

Formula

G.f.: exp(Sum_{k>=1} A062205(k) * x^k/k).