A384360 Expansion of Product_{k>=1} 1/(1 - k*(k+1)*(k+2)/6 * x)^((1/192) * (3/4)^k).

1, 1, 424, 998584, 6925040260, 105920615923684, 3026129933925315784, 144928319460945421096936, 10782220800085014574469693026, 1177609713750570874317795178806210, 180749886489278186545417627942230436008, 37658177020555445685152123914054243838809128

Offset

0,3

Links

Table of n, a(n) for n=0..11.

Formula

G.f.: exp((1/27) * Sum_{k>=1} A384364(3,k) * x^k/k).

Prog

(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(3, k)*x^k/k)/27))

Crossrefs

Cf. A384364.

Sequence in context: A184766 A250377 A250342 * A232359 A294714 A294712

Adjacent sequences: A384357 A384358 A384359 * A384361 A384362 A384363

Keyword

nonn

Author

Seiichi Manyama, May 27 2025

Status

approved