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%I #4 Dec 25 2013 02:38:39
%S 1,1,9,3375,121550625,3101364196875,1730690595263722640625,
%T 376292999446907764908950466328125,
%U 16950118160085960270323673755750390625,90543986887356385297750500755391437150880164126953125
%N a(n) = denominator of sum_(k=1..n) 1/(2*k-1)^n.
%C The sequence A234144(n)/A234145(n) is Theta(n, n), as defined by _Wolfdieter Lang_.
%H Wolfdieter Lang, <a href="/A164655/a164655.pdf">Theta(k, n), k-family of rational sequences and limits.</a>
%F a(n) = denominator of (2^n*Zeta(n) - Zeta(n) - Zeta(n, n+1/2))/2^n.
%F a(n) = denominator of ((-1/2)^n*(PolyGamma(n-1, 1/2) - PolyGamma(n-1, n+1/2)))/(n-1)!.
%F A234144(n) / A234145(n) ~ 1.
%t a[n_] := Sum[1/(2*k-1)^n, {k, 1, n}] // Denominator; Table[a[n], {n, 0, 10}]
%Y Cf. A164655, A164656, A234144 (numerators).
%K nonn,frac,easy
%O 0,3
%A _Jean-François Alcover_, Dec 20 2013
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