OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..500
FORMULA
a(n) = (binomial(4*n, 2*n)+(-1)^n*binomial(2*n, n))/2.
Recurrence: n*(n-1)*(2*n-1)*(5*n^2-15*n+11)*a(n)-4*(n-1)*(30*n^4-120*n^3+161*n^2-82*n+12)*a(n-1)-4*(4*n-7)*(2*n-3)*(4*n-5)*(5*n^2-5*n+1)*a(n-2) = 0.
a(n) ~ 2^(4*n-3/2)/sqrt(Pi*n). - Vaclav Kotesovec, Aug 02 2017
MATHEMATICA
Table[Sum[Binomial[2n, 2k]^2, {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Jan 21 2016 *)
PROG
(Maxima) makelist((binomial(4*n, 2*n)+(-1)^n*binomial(2*n, n))/2, n, 0, 12); /* Emanuele Munarini, Feb 01 2017 */
(PARI) a(n) = sum(k=0, n, binomial(2*n, 2*k)^2); \\ Michel Marcus, Feb 01 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Oct 03 2004
STATUS
approved