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

Author

Artur Jasinski, Mar 03 2010

Keywords

• nonn
• frac

Links

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

Crossrefs

For the denominators see A120268.

Programs

Magma

[0] cat [Numerator((&+[4/(2*k+1)^2: k in [0..n-2]])): n in [2..20]]; // 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 *)

PARI

for(n=1,20, print1(numerator(sum(k=0,n-2, 4/(2*k+1)^2)), ", ")) \\ G. C. Greubel, Aug 23 2018

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