This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A277234 #18 Nov 15 2016 03:57:10
%S A277234 1,3,435,1855,1678635,8178093,831557727,4362807735,26663516457435,
%T A277234 146862472576105,13439367283090749,76661183599555737,
%U A277234 54390019021528255975,318658997759516188425,27581665786275463543575,165068987339858265879975,7173478080571052213369487675
%N A277234 Numerators of partial sums of a Ramanujan series converging to 2/Pi = A060294.
%C A277234 The denominators seem to be A241756.
%C A277234 One of Ramanujan's series is 1 - 5*(1/2)^3 + 9*(1*3/(2*4))^3 - 13*(1*3*5/(2*4*6))^3 +- ... = Sum_{k>=0} (-1)^k*(1+4*k)*(risefac(1/2,k)/k!)^3 where risefac(x,k) = Product_{j=0..k-1} (x+j), and risefac(x,0) = 1. See the Hardy reference, p. 7, eq. (1.2) and p. 105, eq. (7.4.2) for s=1/2. The limit is Buffon's constant 2/Pi given in A060294.
%D A277234 G. H. Hardy, Ramanujan, AMS Chelsea Publ., Providence, RI, 2002, pp. 7, 105.
%F A277234 a(n) = numerator(r(n)), with the rationals r(n) = Sum_{k=0..n} (-1)^k*(1+4*k)*(risefac(1/2,k)/k!)^3 = Sum_{k=0..n} (1+4*k)*(binomial(-1/2,k))^3 = Sum_{k=0..n} (-1)^k*(1+4*k)*((2*k-1)!!/(2*k)!!)^3. The rising factorial has been defined in a comment above. The double factorials are given in A001147 and A000165 with (-1)!! := 1.
%e A277234 The rationals r(n) begin: 1, 3/8, 435/512, 1855/4096, 1678635/2097152, 8178093/16777216, 831557727/1073741824, 4362807735/8589934592, ...
%e A277234 The limit r(n), n -> oo, is 2/Pi = 0.6366197723... given in A060294.
%Y A277234 Cf. A060294, A241756, A277232.
%K A277234 nonn,frac,easy
%O A277234 0,2
%A A277234 _Wolfdieter Lang_, Nov 13 2016