cp's OEIS Frontend

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.

A130551 Numerators of partial sums for a series of (4/5)*Zeta(3).

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%I A130551 #9 Aug 29 2019 16:29:10
%S A130551 1,23,1039,58157,1454021,6854599,30564710941,244517610353,
%T A130551 37411196579209,64619338818497,86008340157931507,8951094220597141,
%U A130551 334314418075511195849,334314418069194908729,48475590620225838341897
%N A130551 Numerators of partial sums for a series of (4/5)*Zeta(3).
%C A130551 The rationals r(n):=2*sum(((-1)^(j-1))/((j^3)*binomial(2*j,j)),j=1..n), tend for n->infinity, to (4/5)*Zeta(3), which is approximately 0.9616455224. See the van der Poorten reference.
%C A130551 The denominators are given in A130552.
%D A130551 A. van der Poorten, A proof that Euler missed..., Math. Intell. 1(1979)195-203; reprinted in Pi: A Source Book, pp. 439-447, eq. 2, with a proof in section 3 and further references in footnote 4.
%D A130551 L. Berggren, T. Borwein and P. Borwein, Pi: A Source Book, Springer, New York, 1997, p. 687.
%H A130551 W. Lang, <a href="/A130551/a130551.txt">Rationals and limit</a>.
%F A130551 a(n)=numerator(r(n)), n>=1, with the rationals r(n) defined above and taken in lowest terms.
%e A130551 Rationals r(n): [1, 23/24, 1039/1080, 58157/60480, 1454021/1512000, ...].
%K A130551 nonn,frac,easy
%O A130551 1,2
%A A130551 _Wolfdieter Lang_, Jul 13 2007