A069985 Numerator of b(n) = binomial(2n,n)^3*(42n+5)/2^(12n+4).

5, 47, 2403, 16375, 7417375, 53760105, 3167882487, 23607123111, 90865711740375, 687802362944125, 41879801005939325, 320193409525211313, 157265345845813485371, 1210756529837794953125, 74775114531441956109375, 578623856286382884714375, 18377920150990405063058370375

Offset

0,1

Links

Amiram Eldar, Table of n, a(n) for n = 0..555

Srinivasa Ramanujan, Modular equations and approximations to Pi, Quart. J. Math., Vol. 45 (1914), pp. 350-372. See p. 45, eq. (29).

Formula

Sum_{n>=0} b(n) = 1/Pi (Ramanujan, 1914).

Example

Fractions begin with 5/16, 47/8192, 2403/33554432, 16375/17179869184, 7417375/562949953421312, 53760105/288230376151711744, ...

Mathematica

a[n_] := Numerator[Binomial[2 n, n]^3*(42 n + 5)/2^(12 n + 4)]; Array[a, 15, 0] (* Amiram Eldar, Apr 29 2022 *)

Crossrefs

Cf. A049541, A069986 (denominators).

Sequence in context: A159480 A196460 A093612 * A300336 A086776 A259502

Adjacent sequences: A069982 A069983 A069984 * A069986 A069987 A069988

Keyword

easy,frac,nonn

Author

Benoit Cloitre, May 01 2002

Status

approved