A145631 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=12.

150, 21651, 15588874, 31427171529, 452551270138, 716841211899677, 1341926748676207290, 3864749036187477202407, 7095679230440208145951582, 6471259458161469829121064993, 931861361975251655393445326142

Offset: 1

Author

Artur Jasinski, Oct 14 2008

Keywords

• frac
• nonn

Comments

For denominators see A145632. For general properties of A_l(x) see A145609.

Crossrefs

Cf. A145609 - A145640.

Programs

Mathematica

m = 12; 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_]:=m^n(Log[m/(m-1)]-Beta[1/m,1+n,0])
Table[12 a[2 n, 12] // FullSimplify // Numerator,{n,1,10}] (* Gerry Martens , Jun 04 2016 *)

Extensions

Edited by R. J. Mathar, Aug 21 2009