A145624 Denominator of the polynomial A_l(x) = Sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=8.

1, 3, 15, 105, 315, 3465, 45045, 18018, 153153, 14549535, 14549535, 334639305, 1673196525, 5019589575, 145568097675, 18050444111700, 265447707525, 265447707525, 9821565178425, 9821565178425, 57526310330775

Offset

1,2

Comments

For numerators see A145623. For general properties of A_l(x) see A145609.

Links

Robert Israel, Table of n, a(n) for n = 1..1150

Formula

Sum_{n >= 1} (A145623(n)/a(n))*x^n = (32*sqrt(x)*log((1+sqrt(x))/(1-sqrt(x))) - 4*log(1-x))/(1-64*x). - Robert Israel, Mar 09 2016

Maple

G:= (32*sqrt(x)*ln((1-sqrt(x))/(1+sqrt(x))) + 4*ln(1-x))/(64*x-1):
S:=series(G, x, 101):
seq(denom(coeff(S, x, n)), n=1..100); # Robert Israel, Mar 09 2016

Mathematica

m = 8; aa = {}; Do[k = 0; Do[k = k + m^(2 r + 1 - d)/d, {d, 1, 2 r}]; AppendTo[aa, Denominator[k]], {r, 1, 30}]; aa (* Artur Jasinski, Oct 14 2008 *)

Crossrefs

Cf. A145609 - A145640.

Sequence in context: A354299 A293996 A229726 * A025547 A352395 A350670

Adjacent sequences: A145621 A145622 A145623 * A145625 A145626 A145627

Keyword

frac,nonn

Author

Artur Jasinski, Oct 14 2008

Extensions

Edited by R. J. Mathar, Aug 21 2009

Status

approved