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A145623 Numerator of the polynomial A_l(x) = Sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=8.

%I A145623 #20 Jul 04 2017 14:37:22
%S A145623 68,13126,4200532,1881839401,361313167484,254364469931206,
%T A145623 211631238983010892,5417759717965164721,2947261286573050252868,
%U A145623 17919348622364145592266214,1146838311831305317954669876
%N A145623 Numerator of the polynomial A_l(x) = Sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=8.
%C A145623 For denominators see A145624. For general properties of A_l(x) see A145609.
%H A145623 Robert Israel, <a href="/A145623/b145623.txt">Table of n, a(n) for n = 1..375</a>
%F A145623 Sum_{n >= 1} (a(n)/A145624(n))*x^n = (32*sqrt(x)*log((1+sqrt(x))/(1-sqrt(x))) - 4*log(1-x))/(1-64*x). - _Robert Israel_, Mar 09 2016
%p A145623 G:= (32*sqrt(x)*ln((1-sqrt(x))/(1+sqrt(x))) + 4*ln(1-x))/(64*x-1):
%p A145623 S:= series(G, x, 51):
%p A145623 seq(coeff(S,x,n),n=1..50); # _Robert Israel_, Mar 09 2016
%t A145623 m = 8; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Numerator[k]], {r, 1, 25}]; aa (* _Artur Jasinski_, Oct 14 2008 *)
%t A145623 a[n_,m_]:=Integrate[(m-x^n)/(m-x),{x,0,1}]+(m^n-m)Log[m/(m-1)]
%t A145623 Table[8 a[2 n, 8] // Simplify  // Numerator, {n,1,25}]  (* _Gerry Martens_ , Jun 04 2016 *)
%Y A145623 Cf. A145609 - A145640.
%K A145623 frac,nonn
%O A145623 1,1
%A A145623 _Artur Jasinski_, Oct 14 2008
%E A145623 Edited by _R. J. Mathar_, Aug 21 2009