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%I #16 Feb 25 2013 11:35:10
%S 2,0,8,0,32,0,128,0,2560,0,1415168,0,57344,0,118521856,0,5749735424,0,
%T 91546451968,0,1792043646976,0,1982765704675328,0,286994513002496,0,
%U 3187598700536922112,0,4625594563496048066560
%N Numerator of (-1/Pi^n) * integral_{0..1} (log(1-1/x)^n) dx.
%C Conjecture: sequence of denominators is A141459.
%e 2*Pi^2/3, 0, 8*Pi^4/15, 0, 32*Pi^6/21, 0, 128*Pi^8/15, 0, 2560*Pi^10/33, ...
%t a[n_] := (-1/Pi^n)*Numerator[Integrate[Log[1 - 1/x]^n, {x, 0, 1}]]; Table[Print[an = a[n]]; an, {n, 2, 30}]
%Y Cf. A079484 (_Gerry Martens_'s Pari program uses this integral).
%K nonn,frac
%O 2,1
%A _Jean-François Alcover_, Jan 30 2013
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