A021154 Expansion of 1/((1-x)(1-2x)(1-5x)(1-11x)).

1, 19, 256, 3066, 35007, 391545, 4339462, 47896672, 527676853, 5808513711, 63913994508, 703155662118, 7735220904139, 85089973066117, 936002419362994, 10296090191237004, 113257309994958465, 1245831999401562363

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-105,197,-110).

Formula

a(0)=1, a(1)=19, a(2)=256, a(3)=3066, a(n)=19*a(n-1)-105*a(n-2)+ 197*a(n-3)- 110*a(n-4). - Harvey P. Dale, Sep 09 2012

a(0)=1, a(1)=19; for n>1, a(n) = 16*a(n-1) -55*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 07 2013

a(n) = (2*11^(n+3) - 15*5^(n+3) + 40*2^(n+3) - 27)/1080. [Yahia Kahloune, Jul 07 2013]

Mathematica

CoefficientList[Series[1/((1-x)(1-2x)(1-5x)(1-11x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{19, -105, 197, -110}, {1, 19, 256, 3066}, 30] (* Harvey P. Dale, Sep 09 2012 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-5*x)*(1-11*x)))); /* or */ I:=[1, 19, 256, 3066]; [n le 4 select I[n] else 19*Self(n-1)-105*Self(n-2)+197*Self(n-3)-110*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 07 2013

Crossrefs

Sequence in context: A027532 A021394 A016316 * A255722 A016313 A335515

Adjacent sequences: A021151 A021152 A021153 * A021155 A021156 A021157

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved