login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A020982 Expansion of 1/((1-9*x)*(1-10*x)*(1-11*x)). 1

%I #21 Sep 08 2022 08:44:45

%S 1,30,601,10050,151501,2135070,28702801,372684090,4712104501,

%T 58346365110,710428956601,8532288986130,101313313019101,

%U 1191569650755150,13901375026212001,161062105099480170

%N Expansion of 1/((1-9*x)*(1-10*x)*(1-11*x)).

%H G. C. Greubel, <a href="/A020982/b020982.txt">Table of n, a(n) for n = 0..955</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (30,-299,990)

%F If we define f(m,j,x) = Sum_{k=j..m} (binomial(m,k)*stirling2(k,j)*x^(m-k)) then a(n-2)=f(n,2,9), (n>=2). - _Milan Janjic_, Apr 26 2009

%F a(n) = 30*a(n-1) -299*a(n-2) +990*a(n-3), n>=3. - _Vincenzo Librandi_, Mar 18 2011

%F a(n) = 21*a(n-1) -110*a(n-2) +9^n, n>=2. - _Vincenzo Librandi_, Mar 18 2011

%F a(n) = 11^(n+2)/2+9^(n+2)/2-10^(n+2). - _R. J. Mathar_, Mar 20 2011

%t CoefficientList[Series[1/((1-9x)(1-10x)(1-11x)),{x,0,20}],x] (* or *) LinearRecurrence[{30,-299,990},{1,30,601},20] (* _Harvey P. Dale_, Jan 30 2013 *)

%o (PARI) x='x+O('x^30); Vec(1/((1-9*x)*(1-10*x)*(1-11*x))) \\ _G. C. Greubel_, Feb 09 2018

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!(1/((1-9*x)*(1-10*x)*(1-11*x)))); // _G. C. Greubel_, Feb 09 2018

%K nonn

%O 0,2

%A _N. J. A. Sloane_

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)