A093605 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.

0, 1, 1, 11, 13, 211, 271, 1919, 2597, 67843, 95259, 588933, 850251, 10098967, 14904091, 85806311, 128927573, 5792144099, 8834766227, 48605936617, 75096287791, 812156618077, 1268822838961, 6760265315081, 10665172132163

Offset

1,4

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Random Matrix

Formula

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

Example

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

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A046161, A052928.

Sequence in context: A140969 A064759 A238090 * A288304 A155967 A111070

Adjacent sequences: A093602 A093603 A093604 * A093606 A093607 A093608

Keyword

nonn,frac

Author

Eric W. Weisstein, Apr 03 2004

Extensions

More terms from Max Alekseyev, Apr 22 2010

Status

approved