A145621 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=7.

105, 31087, 2538991, 248821433, 21946050833, 11828921402977, 7535022933740305, 3692161237533130831, 1025190103621701235981, 954451986471803883166747, 15589382445706130101521201

Offset: 1

Author

Artur Jasinski, Oct 14 2008

Keywords

• frac
• nonn

Comments

For denominators see A145622. For general properties of A_l(x) see A145609.

Links

• Robert Israel, Table of n, a(n) for n = 1..390

Crossrefs

Cf. A145609 - A145640.

Programs

Maple

f:= n -> numer(add(7^(2*n+1-d)/d, d=1..2*n)):
map(f, [$1..40]); # Robert Israel, Jun 05 2016

Mathematica

m = 7; 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[7 a[2 n, 7] // FullSimplify  // Numerator, {n,1,25}]  (* Gerry Martens , Jun 04 2016 *)

Extensions

Edited by R. J. Mathar, Aug 21 2009