A112098 Denominator of Sum_{i=1..n} 1/C(2*i,i).

1, 2, 3, 60, 420, 630, 13860, 32760, 120120, 2042040, 38798760, 923780, 74364290, 212469400, 150965100, 332727080400, 10314539492400, 3438179830800, 24067258815600, 890488576177200, 890488576177200, 1177742955589200, 1569931359800403600, 2354897039700605400

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/C(2*i, i) = (2*Pi*sqrt(3) + 9)/27.

Example

0, 1/2, 2/3, 43/60, 307/420, 463/630, 10201/13860, 24121/32760, 88453/120120, ... -> (2*Pi*sqrt(3) + 9)/27.

Maple

BB:=n->add(1/binomial(2*i, i), i=1..n): a:=n->denom(BB(n)): seq(a(n), n=0..23); # Zerinvary Lajos, Mar 28 2007

Mathematica

Denominator@ Table[Sum[1/Binomial[2 i, i], {i, n}], {n, 0, 23}] (* Michael De Vlieger, Mar 09 2016 *)

Prog

(PARI) a(n) = denominator(sum(i=1, n, 1/binomial(2*i, i))); \\ Michel Marcus, Mar 09 2016

Crossrefs

Cf. A112098.

Sequence in context: A097961 A145556 A124083 * A144545 A085326 A062308

Adjacent sequences: A112095 A112096 A112097 * A112099 A112100 A112101

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 30 2005

Status

approved