A145613 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.

21, 393, 17731, 2234571, 20111503, 1991042087, 33278851497, 119803867191, 54989975121893, 15672142912044093, 987345003473390379, 204380415719298965303, 9197118707369867504211, 248322205098990353297597

Offset: 1

Author

Artur Jasinski, Oct 14 2008

Keywords

• frac
• nonn

Comments

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

Crossrefs

Cf. A145609 - A145640.

Programs

Maple

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

Mathematica

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 *)
a[n_,m_]:=Integrate[(m-x^n)/(m-x),{x,0,1}]+(m^n-m)Log[m/(m-1)]
Table[3 a[2 n, 3] //FullSimplify //Numerator, {n,1,10}]  (* Gerry Martens , Jun 04 2016 *)

Extensions

Edited by R. J. Mathar, Aug 21 2009