A172591 - OEIS

%I #19 Oct 22 2023 07:49:57

%S 1,1172556,306407299538340,2144953893641078315315520,

%T 178394712594906480448637769546038400,

%U 107858549105202487690102571993535153527817734400

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

%D 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.

%H R. H. Hardin, <a href="/A172591/b172591.txt">Table of n, a(n) for n = 1..19</a>

%F 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

%F 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

%t 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 *)

%o (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

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 06 2010