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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.
10
1, 4, 100, 1600, 193600, 9486400, 2741569600, 2741569600, 1450290318400, 245099063809600, 206128312663873600, 3298053002621977600, 3298053002621977600, 1190597133946533913600, 2001393782164123508761600
OFFSET
0,2
LINKS
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
KEYWORD
frac,nonn
AUTHOR
Artur Jasinski, Mar 04 2010
EXTENSIONS
Name simplified by Peter Luschny, Nov 14 2017
STATUS
approved