A369523 a(n) = n*(n^2 - 1)!.

1, 12, 120960, 5230697472000, 3102242008666197196800000, 61998887798316869577999908025139200000000, 86897409147752508696036023331613625269650404482744320000000000, 15860866523235520512929173666895185100358189521818149024850236796901838028800000000000000

Offset: 1

Author

Thomas Scheuerle, Jan 25 2024

Keywords

• nonn
• easy

Comments

a(n) is the number of ways to fill an n X n square matrix with n^2 distinct elements such that a chosen element is in a designated row (or alternatively a column).

Crossrefs

Cf. A088020, A179268.

Programs

Maple

seq(n*factorial(n^2-1), n=1..8);

Mathematica

Table[n*(n^2-1)!, {n, 1, 8}]

PARI

a(n) = n*(n^2-1)!

Formula

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

a(n) = Integral_{x>=0} x^(n - 1)*exp(-x^(1/n)) dx.