OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..576
C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45.
EXAMPLE
0, 1/2, 25/48, 1129/2160, 63251/120960, 1581371/3024000, 52185743/99792000, ... -> Pi^2/18.
MAPLE
f:= proc(n) local i; denom(add(1/(i^3*binomial(2*i, i)), i=1..n)) end proc:
map(f, [$0..20]); # Robert Israel, Jun 22 2023
MATHEMATICA
Table[Sum[1/(k^3 Binomial[2k, k]), {k, n}], {n, 0, 20}]//Denominator (* Harvey P. Dale, Feb 19 2023 *)
PROG
(PARI) a(n) = denominator(sum(i=1, n, 1/(i^3*binomial(2*i, i)))); \\ Michel Marcus, Mar 10 2016
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Nov 30 2005
EXTENSIONS
Definition corrected (and an incorrect sum deleted) by Wolfdieter Lang, Oct 07 2008
STATUS
approved