A020982 Expansion of 1/((1-9*x)*(1-10*x)*(1-11*x)).

1, 30, 601, 10050, 151501, 2135070, 28702801, 372684090, 4712104501, 58346365110, 710428956601, 8532288986130, 101313313019101, 1191569650755150, 13901375026212001, 161062105099480170

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..955

Index entries for linear recurrences with constant coefficients, signature (30,-299,990)

Formula

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

a(n) = 30*a(n-1) -299*a(n-2) +990*a(n-3), n>=3. - Vincenzo Librandi, Mar 18 2011

a(n) = 21*a(n-1) -110*a(n-2) +9^n, n>=2. - Vincenzo Librandi, Mar 18 2011

a(n) = 11^(n+2)/2+9^(n+2)/2-10^(n+2). - R. J. Mathar, Mar 20 2011

Mathematica

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 *)

Prog

(PARI) x='x+O('x^30); Vec(1/((1-9*x)*(1-10*x)*(1-11*x))) \\ G. C. Greubel, Feb 09 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!(1/((1-9*x)*(1-10*x)*(1-11*x)))); // G. C. Greubel, Feb 09 2018

Crossrefs

Sequence in context: A026308 A081140 A131206 * A024436 A042744 A020980

Adjacent sequences: A020979 A020980 A020981 * A020983 A020984 A020985

Keyword

nonn

Author

N. J. A. Sloane

Status

approved