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

0,2

Comments

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

Links

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

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.

Example

See A294970.

Mathematica

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

Prog

(PARI) for(n=0, 20, print1(denominator(sum(k=0, n, (-1)^k/(2*k+1)^2)), ", ")) \\ G. C. Greubel, Aug 22 2018
(Magma) [Denominator((&+[(-1)^k/(2*k+1)^2: k in [0..n]])): n in [0..20]]; // G. C. Greubel, Aug 22 2018

Crossrefs

Cf. A006752, A294970.

Sequence in context: A079727 A251579 A128492 * A001818 A360435 A369059

Adjacent sequences: A294968 A294969 A294970 * A294972 A294973 A294974

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Nov 15 2017

Status

approved