A238796 - OEIS

%I #8 Mar 10 2014 04:15:26

%S 1,1,2,10,52,326,2256,17102,139448,1210582,11116360,107154092,

%T 1080800788,11345351096,123697222208,1395340522214,16260899226608,

%U 195214269203174,2411419562368344,30583990129966436,397876675010548832,5300483255653341714

%N Symmetric (0,1)-matrices of order n where the numbers of 1's is equal to the order n.

%C For n = 3, we have the following 10 matrices:

%C   1 0 0  1 1 0  1 0 1  1 0 0  0 1 0

%C   0 1 0  1 0 0  0 0 0  0 0 1  1 1 0

%C   0 0 1, 0 0 0, 1 0 0, 0 1 0, 0 0 0,

%C ,

%C   0 0 0  0 0 1  0 1 0  0 0 1  0 0 0

%C   0 1 1  0 1 0  1 0 0  0 0 0  0 0 1

%C   0 1 0, 1 0 0, 0 0 1, 1 0 1, 0 1 1

%F a(n) = [x^n](1+x)^n*(1+x^2)^binomial(n, 2).

%F a(n) = sum( binomial(n, 2k)*binomial(binomial(n, 2), k), k=0..n/2 ).

%F a(n) = sum( binomial(n^2-2k, n-k)*binomial(binomial(n, 2), k)*(-2)^k, k=0..n ).

%t Table[Sum[Binomial[n,2k]Binomial[Binomial[n,2],k],{k,0,Floor[n/2]}],{n,0,100}]

%o (Maxima) makelist(sum(binomial(n,2*k)*binomial(binomial(n,2),k),k,0,n/2),n,0,20);

%K nonn

%O 0,3

%A _Emanuele Munarini_, Mar 05 2014