A173945 a(n) = numerator of (Pi^2)/2 - Zeta(2,(2*n-1)/2), where Zeta is the Hurwitz Zeta function.

0, 4, 40, 1036, 51664, 469876, 57251896, 9723595324, 1951933472, 565732015028, 204698374253288, 205082390523068, 108657935761675952, 13600159324521635284, 122539685111374820056, 103156660296672018389596

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..300

Formula

a(n) = numerator of (Zeta(2, 1/2) - Zeta(2, n-1/2)), where Zeta is the Hurwitz Zeta function. - Peter Luschny, Nov 14 2017

a(n) = numerator of Sum_{k=0..(n-2)} 4/(2*k+1)^2. - G. C. Greubel, Aug 23 2018

Maple

A173945 := n -> numer(add((k+1/2)^(-2), k=0..n-2)):
seq(A173945(n), n=1..16); # Peter Luschny, Nov 14 2017

Mathematica

Table[Numerator[Pi^2/2 - Zeta[2, x/2]], {x, 1, 40, 2}] (* or *)
a[n_] := Numerator[Sum[(k+1/2)^(-2), {k, 0, n-2}]]; Table[a[n], {n, 1, 16}] (* Peter Luschny, Nov 14 2017 *)

Prog

(PARI) for(n=1, 20, print1(numerator(sum(k=0, n-2, 4/(2*k+1)^2)), ", ")) \\ G. C. Greubel, Aug 23 2018
(Magma) [0] cat [Numerator((&+[4/(2*k+1)^2: k in [0..n-2]])): n in [2..20]]; // G. C. Greubel, Aug 23 2018

Crossrefs

For the denominators see A120268.

Sequence in context: A321526 A361057 A013108 * A111846 A290000 A363423

Adjacent sequences: A173942 A173943 A173944 * A173946 A173947 A173948

Keyword

nonn,frac

Author

Artur Jasinski, Mar 03 2010

Status

approved