OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..772
C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45.
FORMULA
3*Sum_{i >= 1} 1/(i^2*C(2*i, i)) = zeta(2) = Pi^2/6.
MAPLE
0, 3/2, 13/8, 197/120, 1105/672, 9211/5600, 130277/79200, 82987349/50450400, ... -> Pi^2/6.
X:= [0, seq(3/(i^2*binomial(2*i, i)), i=1..20)]:
S:= ListTools:-PartialSums(X):
map(numer, S); # Robert Israel, Apr 08 2019
PROG
(PARI) a(n) = numerator(3*sum(i=1, n, 1/(i^2*binomial(2*i, i)))); \\ Michel Marcus, Mar 10 2016
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Nov 30 2005
STATUS
approved