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%I #24 Sep 08 2022 08:45:51
%S 1,4,100,1600,193600,9486400,2741569600,2741569600,1450290318400,
%T 245099063809600,206128312663873600,3298053002621977600,
%U 3298053002621977600,1190597133946533913600,2001393782164123508761600
%N a(n) = denominator of ((Zeta(0,2,2/3) - Zeta(0,2,n+2/3))/9), where Zeta is the Hurwitz Zeta function.
%H G. C. Greubel, <a href="/A173987/b173987.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) = denominator of 2*(Pi^2)/3 - J - Zeta(2,(3*n+2)/3), where Zeta is the Hurwitz Zeta function and J is the constant A173973.
%F a(n) = denominator of Sum_{k=0..(n-1)} 9/(3*k+2)^2. - _G. C. Greubel_, Aug 23 2018
%p a := n -> (Zeta(0,2,2/3) - Zeta(0,2,n+2/3))/9:
%p seq(denom(a(n)), n=0..14); # _Peter Luschny_, Nov 14 2017
%t Table[FunctionExpand[(1/9)*(4*(Pi^2)/3 - Zeta[2, 1/3] - Zeta[2, (3*n + 2)/3])], {n, 0, 20}] // Denominator (* _Vaclav Kotesovec_, Nov 13 2017 *)
%t Denominator[Table[Sum[9/(3*k + 2)^2, {k, 0, n - 1}], {n, 0, 20}]] (* _G. C. Greubel_, Aug 23 2018 *)
%o (PARI) for(n=0,20, print1(denominator(9*sum(k=0,n-1, 1/(3*k+2)^2)), ", ")) \\ _G. C. Greubel_, Aug 23 2018
%o (Magma) [1] cat [Denominator((&+[9/(3*k+2)^2: k in [0..n-1]])): n in [1..20]]; // _G. C. Greubel_, Aug 23 2018
%Y For numerators see A173985.
%Y Cf. A006752, A120268, A173945, A173947, A173948, A173949, A173953, A173955, A173973, A173982, A173983, A173984, A173986.
%K frac,nonn
%O 0,2
%A _Artur Jasinski_, Mar 04 2010
%E Name simplified by _Peter Luschny_, Nov 14 2017
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