

A234144


a(n) = numerator of sum_(k=1..n) 1/(2*k1)^n.


2



0, 1, 10, 3527, 123296356, 3115356499043, 1733194364791766081374, 376470435881775086250915790503469, 16952748458548438370767527584555153032, 90548635884513844033505877600764150558334149264809109
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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), kfamily 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(n1, 1/2)  PolyGamma(n1, n+1/2)))/(n1)!.
A234144(n) / A234145(n) ~ 1.


MATHEMATICA

a[n_] := Sum[1/(2*k1)^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

JeanFrançois Alcover, Dec 20 2013


STATUS

approved



