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A128492 Denominator of Sum_{k=1..n} 1/(2*k-1)^2. 4
1, 9, 225, 11025, 99225, 12006225, 2029052025, 405810405, 117279207045, 42337793743245, 42337793743245, 22396692890176605, 2799586611272075625, 25196279501448680625, 21190071060718340405625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Old definition was "Denominators of partial sums for a series for (Pi^2)/8".

See the comments and the Wolfdieter Lang link.

LINKS

Table of n, a(n) for n=1..15.

Wolfdieter Lang, Rationals and limit.

FORMULA

a(n) = denominator( Pi^2/2 - Zeta(2,(2*n+1)/2) ) for n > 0; see Artur Jasinski in A120268. - Bruno Berselli, Dec 02 2013

Also equals denominator( Pi^2/8 - PolyGamma(1, n+1/2)/4 ). - Jean-François Alcover, Dec 17 2013

EXAMPLE

Fractions begin: 1, 10/9, 259/225, 12916/11025, 117469/99225, 14312974/12006225, 2430898831/2029052025, 487983368/405810405, ... = A120268/A128492.

MATHEMATICA

a[n_] := Pi^2/8 - PolyGamma[1, n+1/2]/4 // Simplify // Denominator; Table[a[n], {n, 1, 15}] (* Jean-François Alcover, Dec 17 2013 *)

PROG

(PARI) a(n) = denominator(sum(k=1, n, 1/(2*k-1)^2)); \\ Michel Marcus, May 09 2020

CROSSREFS

Cf. A120268 (numerators).

Sequence in context: A188662 A079727 A251579 * A294971 A001818 A095363

Adjacent sequences:  A128489 A128490 A128491 * A128493 A128494 A128495

KEYWORD

nonn,frac,easy

AUTHOR

Wolfdieter Lang, Apr 04 2007

EXTENSIONS

Definition replaced with Lang's formula by Bruno Berselli, Dec 02 2013

STATUS

approved

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Last modified June 19 10:58 EDT 2021. Contains 345127 sequences. (Running on oeis4.)