A145627 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=10.

105, 63215, 1053605, 2950094435, 663771248638, 1460296747017355, 135598983651622355, 108479186921297959075, 15367884813850544296195, 29198981146316034164367667, 3406547800403537319177914415

Offset: 1

Author

Artur Jasinski, Oct 14 2008

Keywords

• frac
• nonn

Comments

For denominators see A145629. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

Mathematica

m = 10; 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[10 a[2 n, 10] // FullSimplify // Numerator, {n,1,25}] (* Gerry Martens , Jun 04 2016*)

Extensions

Edited by R. J. Mathar, Aug 21 2009