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%I #11 Sep 08 2022 08:46:20
%S 1,9,225,11025,99225,12006225,2029052025,2029052025,586396035225,
%T 211688968716225,211688968716225,111983464450883025,
%U 2799586611272075625,25196279501448680625,21190071060718340405625,20363658289350325129805625
%N Denominators of the partial sums for the Catalan constant A006752: Sum_{k=0..n} ((-1)^k)/(2*k+1)^2, n >= 0.
%C The corresponding numerators are given in A294970. There details are given.
%H G. C. Greubel, <a href="/A294971/b294971.txt">Table of n, a(n) for n = 0..575</a>
%F a(n) = numerator(r(n)) with the rationals r(n) = Sum_{k=0..n} (-1)^k/(2*k+1)^2.
%F For r(n) in terms of the Hurwitz Zeta function or the trigamma function see A294970.
%e See A294970.
%t Table[Denominator[Sum[(-1)^k/(2*k+1)^2, {k,0,n}]], {n,0,20}] (* _Vaclav Kotesovec_, Nov 15 2017 *)
%o (PARI) for(n=0,20, print1(denominator(sum(k=0,n, (-1)^k/(2*k+1)^2)), ", ")) \\ _G. C. Greubel_, Aug 22 2018
%o (Magma) [Denominator((&+[(-1)^k/(2*k+1)^2: k in [0..n]])): n in [0..20]]; // _G. C. Greubel_, Aug 22 2018
%Y Cf. A006752, A294970.
%K nonn,frac,easy
%O 0,2
%A _Wolfdieter Lang_, Nov 15 2017
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