%I #17 Jan 03 2016 17:25:31
%S 6,76,1000,13870,198626,2902782,43019382,644099772,9719235072,
%T 147565763892,2251664727612,34499268410712,530417801358816,
%U 8179108402119256,126443689966980680,1959067830909571214
%N a(n) = Sum_{i=1..n} binomial(4*i,2*i).
%H Harry J. Smith, <a href="/A066797/b066797.txt">Table of n, a(n) for n = 1..150</a>
%F G.f.: ((1+4*sqrt(x))^(-1/2) + (1-4*sqrt(x))^(-1/2) - 2)/(2-2*x). - _Mark van Hoeij_, May 02 2013
%F Recurrence: n*(2*n-1)*a(n) = (34*n^2 - 33*n + 6)*a(n-1) - 2*(4*n-3)*(4*n-1)*a(n-2). - _Vaclav Kotesovec_, Aug 16 2013
%F a(n) ~ 2^(4*n+3)/(15*sqrt(Pi*n/2)). - _Vaclav Kotesovec_, Aug 16 2013
%o (PARI) { a=0; for (n=1, 150, write("b066797.txt", n, " ", a+=binomial(4*n, 2*n)) ) } \\ _Harry J. Smith_, Mar 27 2010
%K nonn
%O 1,1
%A _Benoit Cloitre_, Jan 18 2002