A172591 Number of 5*n X 2*n 0..1 arrays with row sums 2 and column sums 5.

1, 1172556, 306407299538340, 2144953893641078315315520, 178394712594906480448637769546038400, 107858549105202487690102571993535153527817734400

Offset

1,2

References

Gao, Shanzhen, and Matheis, Kenneth, Closed formulas and integer sequences arising from the enumeration of (0,1)-matrices with row sum two and some constant column sums. In Proceedings of the Forty-First Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 202 (2010), 45-53.

Links

R. H. Hardin, Table of n, a(n) for n = 1..19

Formula

a(n) = 120^(-2n)*Sum_{j=0..2n} Sum_{k=0..2n-j} ((-10)^k*15^(2n-j-k)*(2n)!(5n)!(2n+4j+2k)!/(j!k!(2n-j-k)!(n+2j+k)!*2^(n+2j+k))). - Shanzhen Gao, Feb 16 2010

a(n) ~ sqrt(Pi) * 5^(8*n + 1/2) * n^(10*n + 1/2) / (2^(n-1) * 3^(2*n) * exp(10*n + 2)). - Vaclav Kotesovec, Oct 22 2023

Mathematica

Table[120^(-2*n) * Sum[Sum[((-10)^k * 15^(2*n-j-k)*(2*n)!*(5*n)!*(2*n+4*j+2*k)! / (j!*k!*(2*n-j-k)!*(n+2*j+k)!*2^(n+2*j+k))), {k, 0, 2*n-j}], {j, 0, 2*n}], {n, 1, 12}] (* Vaclav Kotesovec, Oct 22 2023 *)

Prog

(PARI) a(n) = 120^(-2*n)*sum(j=0, 2*n, sum(k=0, 2*n-j, ((-10)^k*15^(2*n-j-k)*(2*n)!*(5*n)!*(2*n+4*j+2*k)!/(j!*k!*(2*n-j-k)!*(n+2*j+k)!*2^(n+2*j+k))))); \\ Michel Marcus, Jan 18 2018

Crossrefs

Sequence in context: A288077 A112043 A114677 * A250962 A210411 A204777

Adjacent sequences: A172588 A172589 A172590 * A172592 A172593 A172594

Keyword

nonn

Author

R. H. Hardin, Feb 06 2010

Status

approved