A145613 - OEIS

%I #13 Jun 05 2016 23:33:01

%S 21,393,17731,2234571,20111503,1991042087,33278851497,119803867191,

%T 54989975121893,15672142912044093,987345003473390379,

%U 204380415719298965303,9197118707369867504211,248322205098990353297597

%N Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=3.

%C For denominators see A145614. For general properties of A_l(x) see A145609.

%p A := proc(l,x) add(x^(l-d)/d,d=1..l-1) ; end: A145613 := proc(n) numer( A(2*n+1,3)) ; end: seq(A145613(n),n=1..20) ; # _R. J. Mathar_, Aug 21 2009

%t m = 3; 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_ *)

%t a[n_,m_]:=Integrate[(m-x^n)/(m-x),{x,0,1}]+(m^n-m)Log[m/(m-1)]

%t Table[3 a[2 n, 3] //FullSimplify //Numerator, {n,1,10}]  (* _Gerry Martens_ , Jun 04 2016 *)

%Y Cf. A145609 - A145640.

%K frac,nonn

%O 1,1

%A _Artur Jasinski_, Oct 14 2008

%E Edited by _R. J. Mathar_, Aug 21 2009