A112099 Numerator of Sum_{i=1..n} 1/(i*C(2*i,i)).

0, 1, 7, 3, 169, 1523, 133, 72623, 87149, 823077, 15638477, 46915441, 13834041, 224803169, 6936783521, 5587964507, 4157445593923, 12472336782289, 170187831339, 71785227258967, 153825486983593, 4905323862699739, 21820233734078929, 5695081004594650211

Offset: 0

Author

N. J. A. Sloane, Nov 30 2005

Keywords

• nonn
• frac

Examples

			0, 1/2, 7/12, 3/5, 169/280, 1523/2520, 133/220, 72623/120120, 87149/144144, .... -> Pi*sqrt(3)/9.
		

Links

• C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45.

Crossrefs

Cf. A112100, A112102, A112103, A130549, A130550, A134805.

Programs

Mathematica

Join[{0},Accumulate[Table[1/(x Binomial[2x,x]),{x,30}]]]//Numerator (* Harvey P. Dale, May 08 2022 *)

PARI

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

Formula

Sum_{i >= 1} 1/(i*C(2*i, i)) = Pi*sqrt(3)/9.

Extensions

Definition corrected by Wolfdieter Lang, Oct 07 2008