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

0,3

Links

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

Formula

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

Mathematica

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

Crossrefs

Cf. A351507, A001044, A384092.

Sequence in context: A351136 A232365 A183551 * A114071 A330134 A210069

Adjacent sequences: A384088 A384089 A384090 * A384092 A384093 A384094

Keyword

nonn

Author

Vaclav Kotesovec, May 19 2025

Status

approved