A172602 - OEIS

%I #25 Oct 24 2023 16:22:11

%S 0,1,399072960,26630804377937061000,49825573548689359631837113344000,

%T 1415189158639246716651027917944817871202200000,

%U 396138136990560832867276344563606859994639454544654153984000

%N Number of 7*n X n 0..1 arrays with row sums 2 and column sums 14

%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 Vaclav Kotesovec, <a href="/A172602/b172602.txt">Table of n, a(n) for n = 1..45</a> (terms 1..13 from R. H. Hardin)

%F a(n) = ((7n)!n!/(2^(7n)))*Sum_{r0=0..n} Sum_{r1=0..n-r0} Sum_{r2=0..n-r0-r1} Sum_{r3=0..n-r0-r1-r2} Sum_{r4=0..n-r0-r1-r2-r3} Sum_{r5=0..n-r0-r1-r2-r3-r4} Sum_{r6=0..n-r0-r1-r2-r3-r4-r5} (1/(r0!r1!r2!r3!r4!r5!r6!(n-r0-r1-r2-r3-r4-r5-r6)!))*((-1)^(-6r1-5r2-4r3-3r4-2r5-r6+7n-7r0)/(7n+6r1+5r2+4r3+3r4+2r5+r6-7n+7r0)!)*((14r0+12r1+10r2+8r3+6r4+4r5+2r6)!/((14!)^r0*(12!)^r1*(2!10!)^r2*(3!8!)^r3*(4!6!)^r4*(5!4!)^r5*(6!2!)^r6*(7!)^(n-r0-r1-r2-r3-r4-r5-r6))). - _Shanzhen Gao_, Feb 18 2010

%F a(n) ~ sqrt(Pi) * 7^(12*n + 1/2) * n^(14*n + 1/2) / (2^(4*n-1) * 3^(5*n) * 5^(2*n) * 11^n * 13^n * exp(14*n + 13/2)). - _Vaclav Kotesovec_, Oct 24 2023

%t Table[(7*n)!*n!/2^(7*n) * Sum[Sum[Sum[Sum[Sum[Sum[Sum[ 1/(r0!*r1!*r2!*r3!*r4!*r5!*r6! * (n-r0-r1-r2-r3-r4-r5-r6)!) * ((-1)^(-6*r1-5*r2-4*r3-3*r4-2*r5-r6+7*n-7*r0) / (7*n+6*r1+5*r2+4*r3+3*r4+2*r5+r6-7*n+7*r0)!) * ((14*r0+12*r1+10*r2+8*r3+6*r4+4*r5+2*r6)! / ((14!)^r0*(12!)^r1*(2!10!)^r2*(3!8!)^r3*(4!6!)^r4*(5!4!)^r5*(6!2!)^r6*(7!)^(n-r0-r1-r2-r3-r4-r5-r6))), {r6,0,n-r0-r1-r2-r3-r4-r5}], {r5,0,n-r0-r1-r2-r3-r4}], {r4,0,n-r0-r1-r2-r3}], {r3,0,n-r0-r1-r2}], {r2,0,n-r0-r1}], {r1,0,n-r0}], {r0,0,n}], {n,1,10}] (* _Vaclav Kotesovec_, Oct 23 2023 *)

%K nonn

%O 1,3

%A _R. H. Hardin_, Feb 06 2010