A066797 a(n) = Sum_{i=1..n} binomial(4*i,2*i).

6, 76, 1000, 13870, 198626, 2902782, 43019382, 644099772, 9719235072, 147565763892, 2251664727612, 34499268410712, 530417801358816, 8179108402119256, 126443689966980680, 1959067830909571214

Offset: 1

Author

Benoit Cloitre, Jan 18 2002

Keywords

• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 1..150

Programs

PARI

{ a=0; for (n=1, 150, write("b066797.txt", n, " ", a+=binomial(4*n, 2*n)) ) } \\ Harry J. Smith, Mar 27 2010

Formula

G.f.: ((1+4*sqrt(x))^(-1/2) + (1-4*sqrt(x))^(-1/2) - 2)/(2-2*x). - Mark van Hoeij, May 02 2013

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

a(n) ~ 2^(4*n+3)/(15*sqrt(Pi*n/2)). - Vaclav Kotesovec, Aug 16 2013