%I #13 Oct 02 2018 00:13:46

%S 0,1,1,11,13,211,271,1919,2597,67843,95259,588933,850251,10098967,

%T 14904091,85806311,128927573,5792144099,8834766227,48605936617,

%U 75096287791,812156618077,1268822838961,6760265315081,10665172132163

%N Numerators of sqrt(2) term in expected number of complex eigenvalues in an n X n real matrix with entries chosen from a standard normal distribution.

%C Related to factored form of Beta[ -1,n,3/2].

%H G. C. Greubel, <a href="/A093605/b093605.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RandomMatrix.html">Random Matrix</a>

%F a(n+1) = Sum_{k=0..floor(n/2)} ((C(2*(n-2*k),n-2*k)*16^k)/Sum_{k=0..n, mod(C(n,k),2)). - _Paul Barry_, Oct 26 2007

%e 0, 2-sqrt(2), 2-sqrt(2)/2, 4-(11*sqrt(2))/8, 4-(13*sqrt(2))/16, 6-(211*sqrt(2))/128, ...

%t Table[Sum[(2^(4*k)*Binomial[2*(n-2*k-1), n-2*k-1])/Sum[Mod[Binomial[n - 1, j], 2], {j, 0, n - 1}], {k, 0, Floor[(n - 1)/2]}], {n, 0, 50}] (* _G. C. Greubel_, Oct 01 2018 *)

%o (PARI) for(n=0,30, print1(sum(k=0,floor((n-1)/2), 2^(4*k)*binomial(2*(n-2*k-1), n-2*k-1)/sum(j=0,n-1, lift(Mod(binomial(n-1,j),2)))), ", ")) \\ _G. C. Greubel_, Oct 01 2018

%Y Cf. A046161, A052928.

%K nonn,frac

%O 1,4

%A _Eric W. Weisstein_, Apr 03 2004

%E More terms from _Max Alekseyev_, Apr 22 2010