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
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Apr 03 2004
EXTENSIONS
More terms from Max Alekseyev, Apr 22 2010
STATUS
approved