A306729 a(n) = Product_{i=0..n, j=0..n} (i! + j!).
2, 16, 5184, 9559130112, 109045776752640000000000, 27488263744928988967331390258832998400000000000, 1147897050240877062218236820013018349788772091106840426434074807527014400000000000000
Offset: 0
Keywords
Programs
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Mathematica
Table[Product[i! + j!, {i, 0, n}, {j, 0, n}], {n, 0, 7}] Clear[a]; a[n_] := a[n] = If[n == 0, 2, a[n-1] * Product[k! + n!, {k, 0, n}]^2 / (2*n!)]; Table[a[n], {n, 0, 7}] (* Vaclav Kotesovec, Mar 27 2019 *) Table[Product[Product[k! + j!, {k, 0, j}], {j, 1, n}]^2 / (2^(n-1) * BarnesG[n + 2]), {n, 0, 7}] (* Vaclav Kotesovec, Mar 27 2019 *) -
Python
from math import prod, factorial as f def a(n): return prod(f(i)+f(j) for i in range(n) for j in range(n)) print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Feb 16 2021
Formula
a(n) ~ c * 2^(n^2/2 + 2*n) * Pi^(n^2/2 + n) * n^(2*n^3/3 + 2*n^2 + 11*n/6 + 5/2) / exp(8*n^3/9 + 2*n^2 + n), where c = A324569 = 62.14398692334529025548974541735...
a(n) = a(n-1) * A323717(n)^2 / (2*n!). - Vaclav Kotesovec, Mar 28 2019