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

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%I A384092 #6 May 19 2025 11:49:11
%S A384092 1,1,67,19316,14842986,23959995900,70300141076691,340026368533209120,
%T A384092 2526875675012579004324,27358621384723375076245950,
%U A384092 414013875603209906596527455633,8469874364125222067804767445806552,227937197746419681734617268030982470980,7887251806534473871432104574423885714752540
%N A384092 a(n) = [x^n] Product_{k=1..n} 1/(1 - k^2*x)^n.
%F A384092 a(n) ~ exp(n + 12/5) * n^(3*n - 1/2) / (sqrt(2*Pi) * 3^n).
%t A384092 Table[SeriesCoefficient[Product[1/(1-k^2*x)^n, {k, 0, n}], {x, 0, n}], {n, 0, 15}]
%Y A384092 Cf. A351508, A298851, A384091.
%K A384092 nonn
%O A384092 0,3
%A A384092 _Vaclav Kotesovec_, May 19 2025