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A173985 a(n) = numerator of (Zeta(0,2,2/3) - Zeta(0,2,n+2/3)), where Zeta is the Hurwitz Zeta function. 4
0, 9, 261, 4401, 546921, 27234729, 7956214281, 8017899597, 4266143013213, 724241322449397, 611292843754229277, 9809672294036025657, 9833902887524676921, 3557459561652307818081, 5990804897343048247416561 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

All numbers in this sequence are divisible by 9.

LINKS

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

FORMULA

a(n) = numerator of 2*(Pi^2)/3 - J - Zeta(2, (3*n+2)/3), where Zeta is the Hurwitz Zeta function and the constant J is A173973.

a(n)/A173987(n) = sum_{i=0..n-1} 1/(i+2/3)^2 = psi'(2/3)-psi'(2/3+n). - R. J. Mathar, Apr 22 2010

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

MAPLE

A173985 := proc(n) add( 1/(2/3+i)^2, i=0..n-1) ; numer(%) ; end proc: seq(A173985(n), n=0..20) ; # R. J. Mathar, Apr 22 2010

MATHEMATICA

Table[FunctionExpand[4*(Pi^2)/3 - Zeta[2, 1/3] - Zeta[2, (3*n + 2)/3]], {n, 0, 20}] // Numerator (* Vaclav Kotesovec, Nov 13 2017 *)

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

PROG

(PARI) for(n=0, 20, print1(numerator(9*sum(k=0, n-1, 1/(3*k+1)^2)), ", ")) \\ G. C. Greubel, Aug 23 2018

(MAGMA) [0] cat [Numerator((&+[9/(3*k+1)^2: k in [0..n-1]])): n in [1..20]]; // G. C. Greubel, Aug 23 2018

CROSSREFS

For denominators see A173987.

For A173985/9 see A173986.

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

Sequence in context: A229259 A117796 A117051 * A280178 A189643 A003387

Adjacent sequences:  A173982 A173983 A173984 * A173986 A173987 A173988

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 24 22:45 EST 2022. Contains 350565 sequences. (Running on oeis4.)