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
Keywords
Programs
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Mathematica
Table[SeriesCoefficient[Product[1/(1-k^2*x)^n, {k, 0, n}], {x, 0, n}], {n, 0, 15}]
Formula
a(n) ~ exp(n + 12/5) * n^(3*n - 1/2) / (sqrt(2*Pi) * 3^n).