A145611 Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=2.

5, 131, 1327, 148969, 89422, 7869871, 204620705, 32739453941, 556571247527, 42299423848079, 84598851790183, 31132377803126339, 155661889412050564, 3735885348093583561, 216681350219210744683, 429895798848743086730197

Offset

1,1

Comments

For denominators see A145612. For general properties of A_l(x) see A145609.

Links

Table of n, a(n) for n=1..16.

Maple

A := proc(l, x) add(x^(l-d)/d, d=1..l-1) ; end: A145611 := proc(n) numer( A(2*n+1, 2)) ; end: seq(A145611(n), n=1..20) ; # R. J. Mathar, Aug 21 2009

Mathematica

m = 2; 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, Oct 14 2008 *)
a[n_, m_]:=Integrate[(m-x^n)/(m-x), {x, 0, 1}]+(m^n-m)Log[m/(m-1)]
Table[2 a[2 n, 2] // Simplify  // Numerator, {n, 1, 25}]  (* Gerry Martens , Jun 04 2016 *)

Crossrefs

Cf. A145609 - A145640.

Sequence in context: A203702 A142892 A229879 * A222880 A070247 A171375

Adjacent sequences: A145608 A145609 A145610 * A145612 A145613 A145614

Keyword

frac,nonn

Author

Artur Jasinski, Oct 14 2008

Extensions

Edited by R. J. Mathar, Aug 21 2009

Status

approved