A022453 Expansion of 1/((1-x)*(1-5*x)*(1-7*x)*(1-9*x)).

1, 22, 320, 3890, 42861, 444612, 4433080, 43016380, 409466321, 3843870602, 35717758440, 329381322270, 3020187550381, 27573503381992, 250911867832400, 2277497319225560, 20632700169031041, 186641825267602782

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (22,-164,458,-315).

Formula

a(n) = (3*9^(n+3) - 8*7^(n+3) + 6*5^(n+3) -1)/192. -Yahia Kahloune, Jun 26 2013

a(0)=1, a(1)=22, a(2)=320, a(3)=3890; for n>3, a(n) = 22*a(n-1) -164*a(n-2) +458*a(n-3) -315*a(n-4). - Vincenzo Librandi, Jul 12 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 5 x) (1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 12 2013 *)

Prog

(Magma) I:=[1, 22, 320, 3890]; [n le 4 select I[n] else 22*Self(n-1)-164*Self(n-2)+458*Self(n-3)-315*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-5*x)*(1-7*x)*(1-9*x)))); // Vincenzo Librandi, Jul 12 2013
(PARI) x='x+O('x^30); Vec(1/((1-x)*(1-5*x)*(1-7*x)*(1-9*x))) \\ G. C. Greubel, Feb 28 2018

Crossrefs

Sequence in context: A023949 A025972 A028029 * A025968 A025948 A021904

Adjacent sequences: A022450 A022451 A022452 * A022454 A022455 A022456

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved