A112093 Numerator of 3*Sum_{i=1..n} 1/(i^2*C(2*i,i)).

0, 3, 13, 197, 1105, 9211, 130277, 82987349, 331950131, 16929464521, 29241805241, 3538258509761, 6259995854281, 1057939300471201, 1057939300716589, 51133732870640471, 372975463296151087, 107789908892879155343, 51058377896658637853, 681986753565766904623961

Offset: 0

Author

N. J. A. Sloane, Nov 30 2005

Keywords

• nonn
• frac

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.

Crossrefs

Cf. A112094.

Programs

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

PARI

a(n) = numerator(3*sum(i=1, n, 1/(i^2*binomial(2*i, i)))); \\ Michel Marcus, Mar 10 2016

Formula

3*Sum_{i >= 1} 1/(i^2*C(2*i, i)) = zeta(2) = Pi^2/6.