A021804 Expansion of 1/((1-x)(1-4x)(1-6x)(1-7x)).

1, 18, 213, 2098, 18669, 155946, 1248661, 9704706, 73804797, 552214234, 4080381669, 29857556274, 216794571085, 1564401539082, 11232205936437, 80315244188002, 572351251736733, 4067348923173690, 28836875054284165

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (18,-111,262,-168).

Formula

G.f.: 1/((1-x)*(1-4*x)*(1-6*x)*(1-7*x)).

a(n) = -1/90 +2^(2n+5)/9 -2^(n+2)*3^(n+3)/5 +7^(n+3)/18. [Bruno Berselli, May 08 2013]

a(0)=1, a(1)=18, a(2)=213, a(3)=2098, a(n)=18*a(n-1)-111*a(n-2)+ 262*a(n-3)- 168*a(n-4). - Harvey P. Dale, May 28 2015

Mathematica

CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 6 x) (1 - 7 x)), {x, 0, 20}], x] (* Bruno Berselli, May 08 2013 *)
LinearRecurrence[{18, -111, 262, -168}, {1, 18, 213, 2098}, 30] (* Harvey P. Dale, May 28 2015 *)

Prog

(PARI) Vec(1/((1-x)*(1-4*x)*(1-6*x)*(1-7*x))+O(x^20)) \\ Bruno Berselli, May 08 2013
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-6*x)*(1-7*x)))); // Bruno Berselli, May 08 2013

Crossrefs

Cf. A019316 (first differences).

Sequence in context: A261484 A004323 A025937 * A025932 A260569 A125430

Adjacent sequences: A021801 A021802 A021803 * A021805 A021806 A021807

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved