A173790 a(n) is the number of (0,1) matrices A=(a_{ij}) of size n X (4n) such that each row has exactly four 1's and each column has exactly one 1 and with the restriction that no 1 stands on the diagonal from a_{11} to a_{22}.

0, 20, 10920, 20790000, 103255152000, 1114503570180000, 23066862702843960000, 836044438958485716960000, 49543884378171403300080000000, 4549287429148856071620622680000000

Offset

1,2

Links

Table of n, a(n) for n=1..10.

Formula

a(n) = Sum_{k=0..n} (-1)^k*(4*n-k)!/(24^(n-k)*6^k)*binomial(n,k). [corrected by Georg Fischer, Sep 01 2022]

a(n) ~ sqrt(Pi) * 2^(5*n + 3/2) * n^(4*n + 1/2) / (3^n * exp(4*n+1)). - Vaclav Kotesovec, Oct 21 2023

Mathematica

Table[(4*n)! Hypergeometric1F1[-n, -4*n, -4] / (2^(3*n) * 3^n), {n, 1, 20}] (* Vaclav Kotesovec, Oct 21 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*(4*n-k)!/(24^(n-k)*6^k)*binomial(n, k)) \\ Georg Fischer, Sep 01 2022

Crossrefs

Sequence in context: A135420 A045811 A086687 * A028667 A201507 A167060

Adjacent sequences: A173787 A173788 A173789 * A173791 A173792 A173793

Keyword

nonn

Author

Shanzhen Gao, Feb 24 2010

Status

approved