A325048 a(n) = Product_{i=0..n, j=0..n} (i!^2 + j!^2).

2, 16, 80000, 17272267776000000, 277884245560378426290863196025651200000000, 3337940951837185557810120427617693521487357301121536848574225250643001642844160000000000

Offset

0,1

Links

Table of n, a(n) for n=0..5.

Formula

a(n) ~ c * 2^(n*(n+3)) * Pi^(n*(n+2)) * n^((n+1)*(2*n+1)*(2*n+3)/3) / exp(2*n*(2*n+3)*(4*n+3)/9), where c = 401.488675138779168689540247334821476110398137334270208637438...

Mathematica

Table[Product[i!^2 + j!^2, {i, 0, n}, {j, 0, n}], {n, 0, 7}]
Clear[a]; a[n_] := a[n] = If[n == 0, 2, a[n-1] * Product[k!^2 + n!^2, {k, 0, n}]^2 / (2*n!^2)]; Table[a[n], {n, 0, 7}]

Prog

(Python)
from math import prod, factorial as f
def a(n): return prod(f(i)**2+f(j)**2 for i in range(n) for j in range(n))
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Feb 16 2021

Crossrefs

Cf. A306729, A324403, A325050.

Sequence in context: A092798 A333540 A258169 * A068916 A093987 A275588

Adjacent sequences: A325045 A325046 A325047 * A325049 A325050 A325051

Keyword

nonn

Author

Vaclav Kotesovec, Mar 26 2019

Status

approved