A145615 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=4.

18, 883, 23566, 5278979, 380087174, 66895348819, 13914232622662, 178102177617521, 4036982692723202, 6136213692944321089, 32726473029037904778, 72260052448115886127009, 2890402097924635887833902

Offset: 1

Author

Artur Jasinski, Oct 14 2008

Keywords

• frac
• nonn

Comments

For denominators see A145616. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

Mathematica

m = 4; 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[4 a[2 n, 4] // FullSimplify  // Numerator, {n,1,25}]  (* Gerry Martens , Jun 04 2016 *)

Extensions

Edited by R. J. Mathar, Aug 21 2009