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%I #12 Aug 31 2023 02:54:18
%S 2,4,18,441,122500,585640000,61740367761072,176956326932345427600,
%T 16411667387809544192807523072,59483286633748316026134239331720597504,
%U 9536532654533775992805729638288082189179486453760,81298938207133741609860679855100783339855352530145447380582400
%N a(n) = Product_{k=0..n} (k! + (n-k)!).
%H G. C. Greubel, <a href="/A323702/b323702.txt">Table of n, a(n) for n = 0..35</a>
%F a(n) ~ 2^(n^2/4 + n + 11/6) * n^(3*n*(n+2)/4 + 1/2) * Pi^((n+1)/2) / exp(3*n*(3*n+4)/8) if n is even.
%F a(n) ~ 2^(n^2/4 + n + 7/12) * n^(3*(n+1)^2 / 4) * Pi^((n+1)/2) / exp(3*n*(3*n+4)/8) if n is odd.
%t Table[Product[k! + (n-k)!, {k, 0, n}], {n, 0, 12}]
%o (PARI) a(n) = prod(k=0, n, k! + (n-k)!); \\ _Michel Marcus_, Jan 24 2019
%o (Magma) [(&*[Factorial(j)+Factorial(n-j): j in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Aug 30 2023
%o (SageMath) [product(factorial(j)+factorial(n-j) for j in range(n+1)) for n in range(21)] # _G. C. Greubel_, Aug 30 2023
%Y Cf. A000178, A323575.
%K nonn
%O 0,1
%A _Vaclav Kotesovec_, Jan 24 2019
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