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a(n) = Product_{k=0..n} (n! + k!).
5

%I #13 Nov 20 2023 04:21:29

%S 2,4,36,4704,23400000,7778123781120,245221791787632844800,

%T 980866487456532919096049664000,

%U 647456833933936977045736601678008811520000,89423837415458106416291101560480526982914768896000000000

%N a(n) = Product_{k=0..n} (n! + k!).

%H G. C. Greubel, <a href="/A323717/b323717.txt">Table of n, a(n) for n = 0..29</a>

%F a(n) ~ 2^((n+3)/2) * Pi^((n+1)/2) * n^((n+1)*(2*n+1)/2) / exp(n^2 + n - 1/12).

%F a(n) ~ 2 * (n!)^(n+1). - _Vaclav Kotesovec_, Mar 28 2019

%t Table[Product[n!+k!, {k, 0, n}], {n, 0, 10}]

%o (Magma) F:= Factorial; [(&*[F(n) + F(j): j in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Aug 30 2023

%o (SageMath) f=factorial; [product(f(n) + f(k) for k in range(n+1)) for n in range(21)] # _G. C. Greubel_, Aug 30 2023

%Y Cf. A036740, A203308, A203483, A323702.

%K nonn

%O 0,1

%A _Vaclav Kotesovec_, Jan 25 2019