A021594 Expansion of 1/((1-x)(1-3x)(1-7x)(1-9x)).

1, 20, 270, 3100, 32711, 328440, 3195340, 30437000, 285695421, 2653625260, 24459281210, 224170373700, 2045792060131, 18609941810480, 168874176353880, 1529560509125200, 13833895100278841, 124980009723284100

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (20,-130,300,-189).

Formula

a(n) = (9^(n+3)-2*7^(n+3)+2*3^(n+3)-1)/96. - Yahia Kahloune, May 23 2013

a(0)=1, a(1)=20; for n>1, a(n) = 16*a(n-1) -63*a(n-2) +(3^n - 1)/2. - Vincenzo Librandi, Jul 11 2013

a(0)=1, a(1)=20, a(2)=270, a(3)=3100; for n>3, a(n) = 20*a(n-1) -130*a(n-2) +300*a(n-3) -189*a(n-4). - Vincenzo Librandi, Jul 11 2013

Mathematica

CoefficientList[Series[1 / ((1  -x) (1 - 3 x) (1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 11 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-7*x)*(1-9*x)))); /* or */ I:=[1, 20, 270, 3100]; [n le 4 select I[n] else 20*Self(n-1)-130*Self(n-2)+300*Self(n-3)-189*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 11 2013

Crossrefs

Sequence in context: A025934 A283517 A180799 * A224248 A019793 A021774

Adjacent sequences: A021591 A021592 A021593 * A021595 A021596 A021597

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved