A021294 Expansion of 1/((1-x)(1-2x)(1-9x)(1-11x)).

1, 23, 368, 5098, 65559, 806541, 9640606, 112964816, 1304876837, 14914020979, 169097614764, 1905464222454, 21368620595635, 238731453906137, 2659135639187642, 29548298847110812, 327711548662770753

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (23,-161,337,-198).

Formula

G.f.: 1/((1-x)(1-2x)(1-9x)(1-11x)).

a(n) = (28*11^(n+3) - 45*9^(n+3) + 80*2^(n+3) - 63)/5040. [Yahia Kahloune, Jul 08 2013]

a(0)=1, a(1)=23, a(2)=368, a(3)=5098; for n>3, a(n) = 23*a(n-1) -161*a(n-2) +337*a(n-3) -198*a(n-4). - Vincenzo Librandi, Jul 08 2013

a(0)=1, a(1)=23; for n>1, a(n) = 20*a(n-1) -99*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 08 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 9 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 08 2013 *)

Prog

(Magma) I:=[1, 23, 368, 5098]; [n le 4 select I[n] else 23*Self(n-1)-161*Self(n-2)+337*Self(n-3)-198*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-9*x)*(1-11*x)))); // Vincenzo Librandi, Jul 08 2013

Crossrefs

Sequence in context: A019672 A021629 A019869 * A019628 A018091 A021279

Adjacent sequences: A021291 A021292 A021293 * A021295 A021296 A021297

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved