|
%I #21 Nov 21 2023 16:30:59
%S 1,2,80,187200,50918400000,2675955409920000000,
%T 40702283662588674048000000000,
%U 250658664786823821917343252480000000000000,832906513114759565863066815448211678822400000000000000000,1919381816160714520414106848157314737202346840876384256000000000000000000000
%N a(n) = Product_{1 <= j <= k <= n} (k^2 + j^2).
%F 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
%t Table[Product[k^2 + j^2, {k, 1, n}, {j, 1, k}], {n, 0, 10}]
%o (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
%Y Suggested by _Omar E. Pol_ from A264596 formula.
%Y Cf. A101686, A203475, A324403.
%K easy,nonn
%O 0,2
%A _Velin Yanev_, Oct 05 2017
|
