A021504 Expansion of 1/((1-x)(1-3x)(1-6x)(1-9x)).

1, 19, 244, 2674, 27055, 261793, 2467018, 22871728, 209866789, 1912958047, 17361652672, 157125321262, 1419351371803, 12805505620381, 115437617402806, 1040066979064876, 9367373410791697, 84346984486082395

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,-117,261,-162).

Formula

a(n) = (5*9^(n+3)-16*6^(n+3)+20*3^(n+3)-9)/720. - Yahia Kahloune, May 21 2013

a(0)=1, a(1)=19; for n>1, a(n) = 15*a(n-1) -54*a(n-2) +(3^n -1)/2. - Vincenzo Librandi, Jul 10 2013

a(0)=1, a(1)=19, a(2)=244, a(3)=2674; for n>3, a(n) = 19*a(n-1) -117*a(n-2) +261*a(n-3) -162*a(n-4). - Vincenzo Librandi, Jul 10 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 6  x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 10 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-6*x)*(1-9*x)))); /* or */ I:=[1, 19, 244, 2674]; [n le 4 select I[n] else 19*Self(n-1)-117*Self(n-2)+261*Self(n-3)-162*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 10 2013

Crossrefs

Sequence in context: A021544 A021772 A019783 * A019512 A025927 A224180

Adjacent sequences: A021501 A021502 A021503 * A021505 A021506 A021507

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved