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a(n) = Product_{i=1..n, j=1..n} (i*(i+1) + j*(j+1)).
1

%I #8 Nov 22 2023 18:05:29

%S 1,4,3072,4682022912,62745927042654535680,

%T 22033340103629170301586112512000000,

%U 479715049773154880180722813201712394999926095872000000,1318058833735625830065875826842622254472987373414662267314001234660163584000000

%N a(n) = Product_{i=1..n, j=1..n} (i*(i+1) + j*(j+1)).

%F a(n) ~ c * 2^(n*(n+2)) * exp(Pi*n*(n+2)/2 - 3*n^2) * n^(2*n^2 - 2 - Pi/4), where c = 0.4952828896469310726828820344381813905230827930914109676983577406850360879...

%t Table[Product[i*(i+1)+j*(j+1), {i, 1, n}, {j, 1, n}], {n, 0, 8}]

%o (Python)

%o from math import prod, factorial

%o def A306728(n): return (prod(i*(i+1)+j*(j+1) for i in range(1,n) for j in range(i+1,n+1))*factorial(n))**2*(n+1)<<n # _Chai Wah Wu_, Nov 22 2023

%Y Cf. A324403, A324443.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Mar 06 2019