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

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. A112099.

Programs

Mathematica

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

PARI

a(n) = denominator(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