A021048 Expansion of 1/((1-x)(1-2x)(1-3x)(1-9x)).

1, 15, 160, 1530, 14071, 127605, 1151470, 10372560, 93381541, 840520395, 7564945180, 68085295590, 612770035411, 5514937460385, 49634458601290, 446710191850620, 4020391920103681, 36183527861539575, 325651752496199800

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (15,-65,105,-54).

Formula

a(n) = (243/112)*9^n - (9/4)*3^n + (8/7)*2^n - 1/16. - Neven Juric, Oct 22 2009

a(0)=1, a(1)=15; for n>1, a(n) = 12*a(n-1) -27*a(n-2) +2^n - 1. - Vincenzo Librandi, Jul 05 2013

a(0)=1, a(1)=15, a(2)=160, a(3)=1530; for n>3, a(n) = 15*a(n-1) -65*a(n-2) +105*a(n-3) -54*a(n-4). - Vincenzo Librandi, Jul 05 2013

Mathematica

CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 3 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 05 2013 *)

Prog

(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-3*x)*(1-9*x)))); /* or */ I:=[1, 15, 160, 1530]; [n le 4 select I[n] else 15*Self(n-1)-65*Self(n-2)+105*Self(n-3)-54*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 05 2013

Crossrefs

Sequence in context: A016297 A206811 A027544 * A095685 A263514 A323292

Adjacent sequences: A021045 A021046 A021047 * A021049 A021050 A021051

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved