A021134 Expansion of 1/((1-x)(1-2x)(1-5x)(1-9x)).

1, 17, 200, 2050, 19731, 184047, 1688890, 15362600, 139076861, 1255760077, 11322184380, 102001381950, 918521058391, 8269232646107, 74435809450670, 669985863300100, 6030190661052321, 54273305406490137

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (17,-89,163,-90).

Formula

a(0)=1, a(1)=17; for n>1, a(n) = 14*a(n-1) -45*a(n-2) +2^n -1. - Vincenzo Librandi, Jul 07 2013

a(0)=1, a(1)=17, a(2)=200, a(3)=2050; for n>3, a(n) = 17*a(n-1) -89*a(n-2) +163*a(n-3) -90*a(n-4). - Vincenzo Librandi, Jul 07 2013

a(n) = (3*9^(n+3) - 14*5^(n+3) +32*2^(n+3) - 21)/672. [Yahia Kahloune, Jul 07 2013]

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 5 x) (1 -  9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 07 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-5*x)*(1-9*x)))); /* or */ I:=[1, 17, 200, 2050]; [n le 4 select I[n] else 17*Self(n-1)-89*Self(n-2)+163*Self(n-3)-90*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 07 2013

Crossrefs

Sequence in context: A244002 A201258 A166216 * A065895 A009479 A279448

Adjacent sequences: A021131 A021132 A021133 * A021135 A021136 A021137

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved