A323702 a(n) = Product_{k=0..n} (k! + (n-k)!).

2, 4, 18, 441, 122500, 585640000, 61740367761072, 176956326932345427600, 16411667387809544192807523072, 59483286633748316026134239331720597504, 9536532654533775992805729638288082189179486453760, 81298938207133741609860679855100783339855352530145447380582400

Offset: 0

Author

Vaclav Kotesovec, Jan 24 2019

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..35

Crossrefs

Cf. A000178, A323575.

Programs

Magma

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

Mathematica

Table[Product[k! + (n-k)!, {k, 0, n}], {n, 0, 12}]

PARI

a(n) = prod(k=0, n, k! + (n-k)!); \\ Michel Marcus, Jan 24 2019

SageMath

[product(factorial(j)+factorial(n-j) for j in range(n+1)) for n in range(21)] # G. C. Greubel, Aug 30 2023

Formula

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.

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.