A112097 Numerator of Sum_{i=1..n} 1/C(2*i,i).

0, 1, 2, 43, 307, 463, 10201, 24121, 88453, 1503743, 28571327, 680271, 54761843, 156462429, 111170677, 245020174253, 7595625419003, 2531875141141, 17723125990639, 655755661678837, 655755661685297, 867289746102097, 1156097231554841431, 1734145847332548163

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

Mathematica

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

Prog

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

Crossrefs

Cf. A112098.

Sequence in context: A062582 A073594 A349927 * A354304 A220270 A240550

Adjacent sequences: A112094 A112095 A112096 * A112098 A112099 A112100

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 30 2005

Status

approved