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A173954 a(n) = denominator of (Zeta(2, 3/4) - Zeta(2, n-1/4)), where Zeta is the Hurwitz Zeta function. 7
1, 9, 441, 53361, 1334025, 481583025, 254757420225, 20635351038225, 19830572347734225, 19830572347734225, 3351366726767084025, 6196677077792338362225, 13688459664843275442155025 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..300

FORMULA

a(n) = denominator of (Pi^2 - 8*Catalan - Zeta(2, (4 n - 1)/4)).

a(n) = denominator of Sum_{k=0..(n-2)} 1/(4*k+3)^2. - G. C. Greubel, Aug 23 2018

MAPLE

r := n -> Zeta(0, 2, 3/4) - Zeta(0, 2, n-1/4):

seq(denom(simplify(r(n))), n=1..13); # Peter Luschny, Nov 14 2017

MATHEMATICA

Table[Denominator[FunctionExpand[-8*Catalan + Pi^2 - Zeta[2, (4*n - 1)/4]]], {n, 1, 20}] (* Vaclav Kotesovec, Nov 14 2017 *)

Denominator[Table[8*n*Sum[(-1 + 4*k + 2*n) / ((-1 + 4*k)^2*(-1 + 4*k + 4*n)^2), {k, 0, Infinity}], {n, 1, 20}]] (* Vaclav Kotesovec, Nov 14 2017 *)

Denominator[Table[Sum[1/(4*k + 3)^2, {k, 0, n-1}], {n, 1, 20}]] (* G. C. Greubel, Aug 23 2018 *)

PROG

(PARI) for(n=1, 20, print1(denominator(sum(k=0, n-2, 1/(4*k+3)^2)), ", ")) \\ G. C. Greubel, Aug 23 2018

(MAGMA) [1] cat [Denominator((&+[1/(4*k+3)^2: k in [0..n-2]])): n in [2..20]]; // G. C. Greubel, Aug 23 2018

CROSSREFS

For numerators see A173953.

The Catalan constant is in A006752.

Cf. A006752, A120268, A173945, A173947, A173948, A173949, A173953, A173955.

Sequence in context: A273889 A167720 A287102 * A239479 A229625 A196965

Adjacent sequences:  A173951 A173952 A173953 * A173955 A173956 A173957

KEYWORD

frac,nonn

AUTHOR

Artur Jasinski, Mar 03 2010

EXTENSIONS

Name simplified by Peter Luschny, Nov 14 2017

STATUS

approved

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Last modified January 19 00:40 EST 2020. Contains 331030 sequences. (Running on oeis4.)