A293290 a(n) = Product_{1 <= j <= k <= n} (k^2 + j^2).
1, 2, 80, 187200, 50918400000, 2675955409920000000, 40702283662588674048000000000, 250658664786823821917343252480000000000000, 832906513114759565863066815448211678822400000000000000000, 1919381816160714520414106848157314737202346840876384256000000000000000000000
Offset: 0
Crossrefs
Suggested by Omar E. Pol from A264596 formula.
Programs
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Mathematica
Table[Product[k^2 + j^2, {k, 1, n}, {j, 1, k}], {n, 0, 10}] -
Sage
[prod([prod([k^2+j^2 for j in range(1,k+1)]) for k in range(1,n+1)]) for n in range(10)] # Danny Rorabaugh, Oct 16 2017
Formula
a(n) ~ sqrt(Gamma(1/4)) * Pi^(-1/8) * 2^(n^2/2 + n - 1/8) * exp(Pi*n*(n+1)/4 - 3*n^2/2 - n + Pi/24) * n^(n*(n+1) + 1/4). - Vaclav Kotesovec, Feb 26 2019