A384092 a(n) = [x^n] Product_{k=1..n} 1/(1 - k^2*x)^n.

1, 1, 67, 19316, 14842986, 23959995900, 70300141076691, 340026368533209120, 2526875675012579004324, 27358621384723375076245950, 414013875603209906596527455633, 8469874364125222067804767445806552, 227937197746419681734617268030982470980, 7887251806534473871432104574423885714752540

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

a(n) ~ exp(n + 12/5) * n^(3*n - 1/2) / (sqrt(2*Pi) * 3^n).

Mathematica

Table[SeriesCoefficient[Product[1/(1-k^2*x)^n, {k, 0, n}], {x, 0, n}], {n, 0, 15}]

Crossrefs

Cf. A351508, A298851, A384091.

Sequence in context: A211961 A144940 A211962 * A263463 A367903 A279798

Adjacent sequences: A384089 A384090 A384091 * A384093 A384094 A384095

Keyword

nonn

Author

Vaclav Kotesovec, May 19 2025

Status

approved