A294971 Denominators of the partial sums for the Catalan constant A006752: Sum_{k=0..n} ((-1)^k)/(2*k+1)^2, n >= 0.

1, 9, 225, 11025, 99225, 12006225, 2029052025, 2029052025, 586396035225, 211688968716225, 211688968716225, 111983464450883025, 2799586611272075625, 25196279501448680625, 21190071060718340405625, 20363658289350325129805625

Offset: 0

Author

Wolfdieter Lang, Nov 15 2017

Keywords

• nonn
• frac
• easy

Comments

The corresponding numerators are given in A294970. There details are given.

Examples

			See A294970.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..575

Crossrefs

Cf. A006752, A294970.

Programs

Magma

[Denominator((&+[(-1)^k/(2*k+1)^2: k in [0..n]])): n in [0..20]]; // G. C. Greubel, Aug 22 2018

Mathematica

Table[Denominator[Sum[(-1)^k/(2*k+1)^2, {k,0,n}]], {n,0,20}] (* Vaclav Kotesovec, Nov 15 2017 *)

PARI

for(n=0,20, print1(denominator(sum(k=0,n, (-1)^k/(2*k+1)^2)), ", ")) \\ G. C. Greubel, Aug 22 2018

Formula

a(n) = numerator(r(n)) with the rationals r(n) = Sum_{k=0..n} (-1)^k/(2*k+1)^2.

For r(n) in terms of the Hurwitz Zeta function or the trigamma function see A294970.