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%I #13 Apr 29 2022 12:01:25
%S 5,47,2403,16375,7417375,53760105,3167882487,23607123111,
%T 90865711740375,687802362944125,41879801005939325,320193409525211313,
%U 157265345845813485371,1210756529837794953125,74775114531441956109375,578623856286382884714375,18377920150990405063058370375
%N Numerator of b(n) = binomial(2n,n)^3*(42n+5)/2^(12n+4).
%H Amiram Eldar, <a href="/A069985/b069985.txt">Table of n, a(n) for n = 0..555</a>
%H Srinivasa Ramanujan, <a href="http://ramanujan.sirinudi.org/Volumes/published/ram06.html">Modular equations and approximations to Pi</a>, Quart. J. Math., Vol. 45 (1914), pp. 350-372. See p. 45, eq. (29).
%F Sum_{n>=0} b(n) = 1/Pi (Ramanujan, 1914).
%e Fractions begin with 5/16, 47/8192, 2403/33554432, 16375/17179869184, 7417375/562949953421312, 53760105/288230376151711744, ...
%t a[n_] := Numerator[Binomial[2 n, n]^3*(42 n + 5)/2^(12 n + 4)]; Array[a, 15, 0] (* _Amiram Eldar_, Apr 29 2022 *)
%Y Cf. A049541, A069986 (denominators).
%K easy,frac,nonn
%O 0,1
%A _Benoit Cloitre_, May 01 2002