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.

A128492 Denominator of Sum_{k=1..n} 1/(2*k-1)^2.

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%I A128492 #23 May 09 2020 19:33:24
%S A128492 1,9,225,11025,99225,12006225,2029052025,405810405,117279207045,
%T A128492 42337793743245,42337793743245,22396692890176605,2799586611272075625,
%U A128492 25196279501448680625,21190071060718340405625
%N A128492 Denominator of Sum_{k=1..n} 1/(2*k-1)^2.
%C A128492 Old definition was "Denominators of partial sums for a series for (Pi^2)/8".
%C A128492 See the comments and the _Wolfdieter Lang_ link.
%H A128492 Wolfdieter Lang, <a href="/A120268/a120268.txt">Rationals and limit</a>.
%F A128492 a(n) = denominator( Pi^2/2 - Zeta(2,(2*n+1)/2) ) for n > 0; see _Artur Jasinski_ in A120268. - _Bruno Berselli_, Dec 02 2013
%F A128492 Also equals denominator( Pi^2/8 - PolyGamma(1, n+1/2)/4 ). - _Jean-François Alcover_, Dec 17 2013
%e A128492 Fractions begin: 1, 10/9, 259/225, 12916/11025, 117469/99225, 14312974/12006225, 2430898831/2029052025, 487983368/405810405, ... = A120268/A128492.
%t A128492 a[n_] := Pi^2/8 - PolyGamma[1, n+1/2]/4 // Simplify // Denominator; Table[a[n], {n, 1, 15}] (* _Jean-François Alcover_, Dec 17 2013 *)
%o A128492 (PARI) a(n) = denominator(sum(k=1, n, 1/(2*k-1)^2)); \\ _Michel Marcus_, May 09 2020
%Y A128492 Cf. A120268 (numerators).
%K A128492 nonn,frac,easy
%O A128492 1,2
%A A128492 _Wolfdieter Lang_, Apr 04 2007
%E A128492 Definition replaced with Lang's formula by _Bruno Berselli_, Dec 02 2013