%I #14 Sep 08 2022 08:44:45

%S 1,22,335,4400,53481,620202,6970675,76624900,828512861,8845504382,

%T 93498427815,980374738200,10212261530641,105799242660562,

%U 1091082072825755,11208627544304300,114766536787594821

%N Expansion of 1/((1-x)(1-2x)(1-9x)(1-10x)).

%H Vincenzo Librandi, <a href="/A021284/b021284.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (22,-149,308,-180)

%F a(n) = (7*10^(n+3) - 9^(n+4) + 9*2^(n+3) - 7)/504. - _Yahia Kahloune_, Jul 08 2013

%F a(0)=1, a(1)=22, a(2)=335, a(3)=4400; for n>3, a(n) = 22*a(n-1) -149*a(n-2) +308*a(n-3) -180*a(n-4). - _Vincenzo Librandi_, Jul 08 2013

%F a(0)=1, a(1)=22; for n>1 a(n) = 19*a(n-1) -90*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 08 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 9 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_ Jul 08 2013 *)

%o (Magma) I:=[1, 22, 335, 4400]; [n le 4 select I[n] else 22*Self(n-1)-149*Self(n-2)+308*Self(n-3)-180*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-9*x)*(1-10*x)))); // _Vincenzo Librandi_, Jul 08 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.