A107447 a(n) = binomial(n!, n^2).

1, 0, 0, 735471, 41749257038001257014137504, 8072776113194557737391130747136885454937928869204466648295480, 34145180671088019813488798475366394184193477615213303683031012996650190080826664983024305988320017979711374101114480000

Offset: 1

Author

Zak Seidov, May 26 2005

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..11

Crossrefs

Cf. A014062 C(n^2, n), A086687 C(n!, n), A067454.

Programs

Magma

[Binomial(Factorial(n), n^2): n in [1..9]]; // G. C. Greubel, Mar 24 2024

Mathematica

a[n_]:= Binomial[n!, n^2]; Array[a, 10]

SageMath

[binomial(factorial(n), n^2) for n in range(1,10)] # G. C. Greubel, Mar 24 2024

Formula

From Vaclav Kotesovec, May 28 2025: (Start)

a(n) ~ n!^(n^2) / (n^2)!.

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