A173987 a(n) = denominator of ((Zeta(0,2,2/3) - Zeta(0,2,n+2/3))/9), where Zeta is the Hurwitz Zeta function.

1, 4, 100, 1600, 193600, 9486400, 2741569600, 2741569600, 1450290318400, 245099063809600, 206128312663873600, 3298053002621977600, 3298053002621977600, 1190597133946533913600, 2001393782164123508761600

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..300

Formula

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.

a(n) = denominator of Sum_{k=0..(n-1)} 9/(3*k+2)^2. - G. C. Greubel, Aug 23 2018

Maple

a := n -> (Zeta(0, 2, 2/3) - Zeta(0, 2, n+2/3))/9:
seq(denom(a(n)), n=0..14); # Peter Luschny, Nov 14 2017

Mathematica

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 *)
Denominator[Table[Sum[9/(3*k + 2)^2, {k, 0, n - 1}], {n, 0, 20}]] (* G. C. Greubel, Aug 23 2018 *)

Prog

(PARI) for(n=0, 20, print1(denominator(9*sum(k=0, n-1, 1/(3*k+2)^2)), ", ")) \\ G. C. Greubel, Aug 23 2018
(Magma) [1] cat [Denominator((&+[9/(3*k+2)^2: k in [0..n-1]])): n in [1..20]]; // G. C. Greubel, Aug 23 2018

Crossrefs

For numerators see A173985.

Cf. A006752, A120268, A173945, A173947, A173948, A173949, A173953, A173955, A173973, A173982, A173983, A173984, A173986.

Sequence in context: A029995 A365608 A244352 * A052144 A165518 A127776

Adjacent sequences: A173984 A173985 A173986 * A173988 A173989 A173990

Keyword

frac,nonn

Author

Artur Jasinski, Mar 04 2010

Extensions

Name simplified by Peter Luschny, Nov 14 2017

Status

approved