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A173987 a(n) = denominator of ((Zeta(0,2,2/3) - Zeta(0,2,n+2/3))/9), where Zeta is the Hurwitz Zeta function. 7
1, 4, 100, 1600, 193600, 9486400, 2741569600, 2741569600, 1450290318400, 245099063809600, 206128312663873600, 3298053002621977600, 3298053002621977600, 1190597133946533913600, 2001393782164123508761600 (list; graph; refs; listen; history; text; internal format)
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: A017090 A029995 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

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Last modified January 18 14:40 EST 2022. Contains 350455 sequences. (Running on oeis4.)