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A234144 a(n) = numerator of sum_(k=1..n) 1/(2*k-1)^n. 2
0, 1, 10, 3527, 123296356, 3115356499043, 1733194364791766081374, 376470435881775086250915790503469, 16952748458548438370767527584555153032, 90548635884513844033505877600764150558334149264809109 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The sequence A234144(n)/A234145(n) is Theta(n, n), as defined by Wolfdieter Lang.

LINKS

Table of n, a(n) for n=0..9.

Wolfdieter Lang, Theta(k, n), k-family of rational sequences and limits.

FORMULA

a(n) = numerator of (2^n*Zeta(n) - Zeta(n) - Zeta(n, n+1/2))/2^n.

a(n) = numerator of ((-1/2)^n*(PolyGamma(n-1, 1/2) - PolyGamma(n-1, n+1/2)))/(n-1)!.

A234144(n) / A234145(n) ~ 1.

MATHEMATICA

a[n_] := Sum[1/(2*k-1)^n, {k, 1, n}] // Numerator; Table[a[n], {n, 0, 10}]

CROSSREFS

Cf. A164655, A164656, A234145 (denominators).

Sequence in context: A006903 A115481 A154238 * A291676 A249851 A024139

Adjacent sequences:  A234141 A234142 A234143 * A234145 A234146 A234147

KEYWORD

nonn,frac,easy

AUTHOR

Jean-François Alcover, Dec 20 2013

STATUS

approved

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Last modified December 1 05:20 EST 2021. Contains 349426 sequences. (Running on oeis4.)