A112100 Denominator of Sum_{i=1..n} 1/(i*C(2*i,i)).

1, 2, 12, 5, 280, 2520, 220, 120120, 144144, 1361360, 25865840, 77597520, 22881320, 371821450, 11473347600, 9242418900, 6876359661600, 20629078984800, 281488407200, 118731810156960, 254425307479200, 8113340360725600, 36090376087365600, 9419588158802421600

Offset

0,2

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

Table[Sum[1/(i*Binomial[2i, i]), {i, n}], {n, 0, 30}]//Denominator (* Harvey P. Dale, May 11 2019 *)

Prog

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

Crossrefs

Cf. A112099.

Sequence in context: A286480 A286256 A239111 * A079080 A228454 A278255

Adjacent sequences: A112097 A112098 A112099 * A112101 A112102 A112103

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 30 2005

Extensions

Definition corrected by Wolfdieter Lang, Oct 07 2008

Status

approved