A131137 Denominator of (exponential) expansion of log((2*x/3-1)/(x-1)).

1, 3, 9, 27, 27, 81, 243, 243, 729, 2187, 729, 2187, 6561, 6561, 19683, 59049, 59049, 177147, 531441, 177147, 531441, 1594323, 1594323, 4782969, 14348907, 14348907, 43046721, 129140163, 14348907, 43046721, 129140163, 129140163, 387420489

Offset

0,2

Comments

a(n) = 3^A131138(n).

Also, starting at second term, denominator of (1-(2/3)^n)*(n-1)!;

Conjecture: starting at third term, also equals the denominator of polylog(-n,1/4)/4. - Wouter Meeussen, Feb 13 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Mathematica

Denominator[CoefficientList[Series[Log[(2 x/3 - 1)/(x - 1)], {x, 0, 32}], x] Range[0, 32]!]; (* or *) Prepend[Table[Denominator[(1 - (2/3)^n) (n - 1)!], {n, 32}], 1]; (* or *) Join[{1, 3}, Table[Denominator[PolyLog[-n, 1/4]/4 ], {n, 31}]] (* Wouter Meeussen, Feb 13 2014 *)

Prog

(PARI) a(n)=if(n<4, 3^n, denominator(polylog(1-n, 1/4)/4)) \\ Charles R Greathouse IV, Jul 15 2014

Crossrefs

Cf. A131136.

Sequence in context: A168427 A070344 A070357 * A370871 A061948 A018644

Adjacent sequences: A131134 A131135 A131136 * A131138 A131139 A131140

Keyword

nonn,easy

Author

Paul Barry, Jun 17 2007

Status

approved