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A112097
Numerator of Sum_{i=1..n} 1/C(2*i,i).
0
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
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 A375157 A220270
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Nov 30 2005
STATUS
approved