A145617 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=5.

55, 8365, 209195, 73218955, 5491423277, 1510141416085, 490795960391965, 24539798019883535, 10429414158454786655, 4953971725266096561953, 11259026648332043641555, 6473940322790925219990095

Offset: 1

Author

Artur Jasinski, Oct 14 2008

Keywords

• frac
• nonn

Comments

For denominators see A145618. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

Mathematica

m = 5; 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[5 a[2 n, 5] // FullSimplify  // Numerator, {n,1,25}]  (* Gerry Martens , Jun 04 2016 *)

Extensions

Edited by R. J. Mathar, Aug 21 2009