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

Author

Benoit Cloitre, May 01 2002

Keywords

• easy
• frac
• nonn

Examples

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

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).

Crossrefs

Cf. A049541, A069986 (denominators).

Programs

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 *)

Formula

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