A325049 a(n) = Product_{i=0..n, j=0..n} (i!*j! + 1).
2, 16, 6480, 97287175440, 1106928595945936328906250000, 856337316801926460412829104011102303451051923953906250000
Offset: 0
Keywords
Programs
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Mathematica
Table[Product[i!*j! + 1, {i, 0, n}, {j, 0, n}], {n, 0, 7}] Table[BarnesG[n+2]^(2*n+2) * Product[1 + 1/(i!*j!), {i, 0, n}, {j, 0, n}], {n, 0, 7}] -
Python
from math import prod, factorial as f def a(n): return prod(f(i)*f(j)+1 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
Formula
a(n) ~ c * (2*Pi)^((n+1)^2) * n^((n+1)*(6*n^2 + 12*n + 5)/6) / (A^(2*n+2) * exp(3*n^3/2 + 7*n^2/2 + 11*n/6 - 1/3)), where c = Product_{i>=0, j>=0} (1 + 1/(i!*j!)) = 297.557220207478770881166673701943476275955597334672817171839377... and A is the Glaisher-Kinkelin constant A074962.