OFFSET
1,1
COMMENTS
Presumably this is the same as A093581? - Andrew S. Plewe, Apr 18 2007
LINKS
Robert Israel, Table of n, a(n) for n = 1..830
Eric Weisstein's World of Mathematics, Gaussian Triangle Picking
FORMULA
From Robert Israel, Sep 29 2016: (Start)
a(n) is the denominator of p(n) = Sum_{k=n..2n-1} binomial(2n-1,k) 3^(2n-k)/4^(2n-1).
-(6n+3)p(n)+(14n+11)p(n+1)-(8n+8)p(n+2)=0 for n >= 1.
G.f. of p(n): 3x(1-1/sqrt(4-3x))/(2-2x). (End)
EXAMPLE
3/4, 15/32, 159/512, 867/4096, 19239/131072, 107985/1048576, ...
MAPLE
p:= gfun:-rectoproc({(-6*n-3)*v(n)+(14*n+11)*v(n+1)+(-8*n-8)*v(n+2), v(0) = 0, v(1) = 3/4, v(2) = 15/32}, v(n), remember):
seq(denom(p(n)), n=1..50); # Robert Israel, Sep 29 2016
MATHEMATICA
a[n_] := (3^n/4^(2n-1)) Binomial[2n-1, n] Hypergeometric2F1[1, 1-n, 1+n, -1/3] // Denominator; Array[a, 20] (* Jean-François Alcover, Mar 22 2019 *)
PROG
(PARI) a(n) = denominator(sum(k=n, 2*n-1, binomial(2*n-1, k)*3^(2*n-k)/4^(2*n-1))); \\ Michel Marcus, Mar 23 2019
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Jan 14 2005
STATUS
approved