A021454 Expansion of 1/((1-x)(1-3x)(1-5x)(1-9x)).

1, 18, 220, 2310, 22561, 212268, 1957600, 17857620, 161924521, 1463379918, 13200803980, 118959425130, 1071396569881, 9646380238968, 86836484875360, 781623699024840, 7035090031526641, 63318194178965418

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,-104,222,-135).

Formula

a(0)=1, a(1)=18, a(2)=220, a(3)=2310, a(n)=18*a(n-1)- 104*a(n-2)+ 222*a(n-3)- 135*a(n-4). - Harvey P. Dale, Nov 05 2011

a(n) = (3*9^(n+2) - 2*5^(n+3) + 8*3^(n+2) - 1)/64. - Yahia Kahloune, Jun 26 2013

a(0)=1, a(1)=18; for n>1, a(n) = 14*a(n-1) -45*a(n-2) +(3^n-1)/2. - Vincenzo Librandi, Jul 10 2013

Mathematica

CoefficientList[Series[1/((1-x)(1-3x)(1-5x)(1-9x)), {x, 0, 20}], x] (* Harvey P. Dale, Nov 05 2011 *)
(* Alternative: *)
LinearRecurrence[{18, -104, 222, -135}, {1, 18, 220, 2310}, 20] (* Harvey P. Dale, Nov 05 2011 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-5*x)*(1-9*x)))); // Vincenzo Librandi, Jul 10 2013

Crossrefs

Sequence in context: A041616 A224296 A019333 * A021224 A017997 A018911

Adjacent sequences: A021451 A021452 A021453 * A021455 A021456 A021457

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved