A384091 a(n) = [x^n] Product_{k=1..n} (1 + k^2*x)^n.
1, 1, 33, 6968, 4503078, 6507545775, 17683339661956, 80849884332530600, 575530003415681613468, 6023356562522188931288775, 88682105895482127774508529242, 1773600518272635675832361778156960, 46830898160739235037404595987069052560, 1594447058825655577475889095097916983404652
Offset: 0
Keywords
Programs
-
Mathematica
Table[SeriesCoefficient[Product[(1+k^2*x)^n, {k, 0, n}], {x, 0, n}], {n, 0, 15}]
Formula
a(n) ~ exp(n + 3/5) * n^(3*n - 1/2) / (sqrt(2*Pi) * 3^n).