A323717 a(n) = Product_{k=0..n} (n! + k!).

2, 4, 36, 4704, 23400000, 7778123781120, 245221791787632844800, 980866487456532919096049664000, 647456833933936977045736601678008811520000, 89423837415458106416291101560480526982914768896000000000

Offset: 0

Author

Vaclav Kotesovec, Jan 25 2019

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..29

Crossrefs

Cf. A036740, A203308, A203483, A323702.

Programs

Magma

F:= Factorial; [(&*[F(n) + F(j): j in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 30 2023

Mathematica

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

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

Formula

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

a(n) ~ 2 * (n!)^(n+1). - Vaclav Kotesovec, Mar 28 2019