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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 08:35 EST 2022. Contains 358515 sequences. (Running on oeis4.)