A128492 Denominator of Sum_{k=1..n} 1/(2*k-1)^2.

1, 9, 225, 11025, 99225, 12006225, 2029052025, 405810405, 117279207045, 42337793743245, 42337793743245, 22396692890176605, 2799586611272075625, 25196279501448680625, 21190071060718340405625

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 A360435

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