A131136 Denominator of (exponential) expansion of log((x/2-1)/(x-1)).

1, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 32, 32, 64, 32, 64, 64, 128, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16

Offset

0,2

Comments

a(n+1) = 2^A063787(n). a(n+1) = A001316(n)/2. - Stephen Crowley, Aug 25 2008

Also, 1 followed by A117973. - Omar E. Pol, Dec 11 2010

Links

Table of n, a(n) for n=0..75.

Formula

a(n) = 0^n + n + Sum_{k=0..n-1} (-1)^(1 + binomial(n-1,k)). - Stephen Crowley, Aug 25 2008

Example

From Omar E. Pol, Jun 14 2009, Dec 11 2010: (Start)
May be written as a triangle by using the Crowley formula with A063787:
.1;
.2;
.4,4;
.8,4,8,8;
.16,4,8,8,16,8,16,16;
.32,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32;
.64,4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,...
Also
1,
2,
4,
4,8,
4,8,8,16,
4,8,8,16,8,16,16,32,
4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,
4,8,8,16,8,16,16,32,8,16,16,32,16,32,32,64,8,16,16,32,16,32,32,64,16,32,...
(End)

Maple

a(n)=abs(op(1, numer(expand(Zeta(2n)/Zeta(1-2n))))) # Stephen Crowley, Aug 25 2008

Mathematica

With[{nn=80}, Denominator[CoefficientList[Series[Log[(x/2-1)/(x-1)], {x, 0, nn}], x] Range[0, nn]!]] (* Harvey P. Dale, Apr 28 2016 *)

Crossrefs

Cf. A001316, A131135.

Cf. A063787.

Cf. A000079, A117973. - Omar E. Pol, Jun 14 2009, Dec 11 2010

Sequence in context: A117215 A011173 A162943 * A117973 A347191 A337256

Adjacent sequences: A131133 A131134 A131135 * A131137 A131138 A131139

Keyword

nonn

Author

Paul Barry, Jun 17 2007

Status

approved