OFFSET
0,3
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+1)/3), where Zeta is the Hurwitz Zeta function and the constant J is A173973.
a(n) = denominator of Sum_{k=1..(n-1)} 9/(3*k+1)^2. - G. C. Greubel, Aug 24 2018
MAPLE
a := n -> Zeta(0, 2, 1/3) - Zeta(0, 2, n+1/3):
seq(denom(a(n)), n=0..14); # Peter Luschny, Nov 14 2017
MATHEMATICA
Table[FunctionExpand[-Zeta[2, (3*n + 1)/3] + Zeta[2, 1/3]], {n, 0, 20}] // Denominator (* Vaclav Kotesovec, Nov 13 2017 *)
Denominator[Table[Sum[9/(3*k + 1)^2, {k, 1, n - 1}], {n, 0, 30}]] (* G. C. Greubel, Aug 24 2018 *)
PROG
(PARI) for(n=0, 20, print1(denominator(sum(k=1, n-1, 9/(3*k+1)^2)), ", ")) \\ G. C. Greubel, Aug 24 2018
(Magma) [1, 1] cat [Denominator((&+[9/(3*k+1)^2: k in [1..n-1]])): n in [2..20]]; // G. C. Greubel, Aug 24 2018
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Artur Jasinski, Mar 04 2010
EXTENSIONS
Name simplified by Peter Luschny, Nov 14 2017
STATUS
approved