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

0,3

Links

Table of n, a(n) for n=0..23.

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A054471 A086453 A320842 * A013324 A110792 A221388

Adjacent sequences: A112096 A112097 A112098 * A112100 A112101 A112102

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 30 2005

Extensions

Definition corrected by Wolfdieter Lang, Oct 07 2008

Status

approved