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%I #12 Nov 06 2023 01:56:03
%S 0,1,10,3527,123296356,3115356499043,1733194364791766081374,
%T 376470435881775086250915790503469,
%U 16952748458548438370767527584555153032,90548635884513844033505877600764150558334149264809109
%N a(n) = numerator 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 Robert Israel, <a href="/A234144/b234144.txt">Table of n, a(n) for n = 0..35</a>
%H Wolfdieter Lang, <a href="/A164655/a164655.pdf">Theta(k, n), k-family of rational sequences and limits</a>.
%F a(n) = numerator of (2^n*Zeta(n) - Zeta(n) - Zeta(n, n+1/2))/2^n.
%F a(n) = numerator of ((-1/2)^n*(PolyGamma(n-1, 1/2) - PolyGamma(n-1, n+1/2)))/(n-1)!.
%F A234144(n) / A234145(n) ~ 1.
%p f:= proc(n) local k; numer(add(1/(2*k-1)^n,k=1..n)); end proc:
%p map(f, [$0..10]); # _Robert Israel_, Nov 05 2023
%t a[n_] := Sum[1/(2*k-1)^n, {k, 1, n}] // Numerator; Table[a[n], {n, 0, 10}]
%Y Cf. A164655, A164656, A234145 (denominators).
%K nonn,frac,easy
%O 0,3
%A _Jean-François Alcover_, Dec 20 2013
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