cp's OEIS Frontend

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

%I A173945 #19 Sep 08 2022 08:45:51
%S A173945 0,4,40,1036,51664,469876,57251896,9723595324,1951933472,565732015028,
%T A173945 204698374253288,205082390523068,108657935761675952,
%U A173945 13600159324521635284,122539685111374820056,103156660296672018389596
%N A173945 a(n) = numerator of (Pi^2)/2 - Zeta(2,(2*n-1)/2), where Zeta is the Hurwitz Zeta function.
%H A173945 G. C. Greubel, <a href="/A173945/b173945.txt">Table of n, a(n) for n = 1..300</a>
%F A173945 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
%F A173945 a(n) = numerator of Sum_{k=0..(n-2)} 4/(2*k+1)^2. - _G. C. Greubel_, Aug 23 2018
%p A173945 A173945 := n -> numer(add((k+1/2)^(-2), k=0..n-2)):
%p A173945 seq(A173945(n), n=1..16); # _Peter Luschny_, Nov 14 2017
%t A173945 Table[Numerator[Pi^2/2 - Zeta[2, x/2]], {x, 1, 40, 2}] (* or *)
%t A173945 a[n_] := Numerator[Sum[(k+1/2)^(-2), {k,0,n-2}]]; Table[a[n], {n,1,16}] (* _Peter Luschny_, Nov 14 2017 *)
%o A173945 (PARI) for(n=1,20, print1(numerator(sum(k=0,n-2, 4/(2*k+1)^2)), ", ")) \\ _G. C. Greubel_, Aug 23 2018
%o A173945 (Magma) [0] cat [Numerator((&+[4/(2*k+1)^2: k in [0..n-2]])): n in [2..20]]; // _G. C. Greubel_, Aug 23 2018
%Y A173945 For the denominators see A120268.
%K A173945 nonn,frac
%O A173945 1,2
%A A173945 _Artur Jasinski_, Mar 03 2010