OFFSET
0,2
LINKS
C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45.
FORMULA
Sum_{i >= 1} 1/(i^2*binomial(2*i, i)) = Pi^2/18.
EXAMPLE
0, 1/2, 13/24, 197/360, 1105/2016, 9211/16800, 130277/237600, 82987349/151351200, ...
MAPLE
seq(denom(add(1/(k^2*binomial(2*k, k)), k = 1 .. n)), n = 0 .. 19); # Peter Bala, Mar 03 2015
MATHEMATICA
Join[{1}, Denominator[Accumulate[Table[1/(n^2 Binomial[2n, n]), {n, 20}]]]] (* Harvey P. Dale, Jun 07 2021 *)
PROG
(PARI) a(n) = denominator(sum(i=1, n, 1/(i^2*binomial(2*i, i)))); \\ Michel Marcus, Mar 10 2016
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Wolfdieter Lang and N. J. A. Sloane, Oct 13 2008
STATUS
approved