A016109 Expansion of 1/((1-7*x)*(1-8*x)*(1-9*x)*(1-10*x)).

1, 34, 725, 12410, 186501, 2571114, 33339685, 413066170, 4941549701, 57504755594, 654463491045, 7314256515930, 80522026412101, 875355238834474, 9415203971344805, 100355146006589690

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (34,-431,2414,-5040).

Formula

If we define f(m,j,x) = Sum_{k=j..m} binomial(m,k)*Stirling2(k,j)*x^(m-k) then a(n-3) = f(n,3,7), n >= 3. - Milan Janjic, Apr 26 2009; adapted by R. J. Mathar, Mar 15 2011

a(n) = 19*a(n-1) - 90*a(n-2) + 8^(n+1) - 7^(n+1), n >= 2. - Vincenzo Librandi, Mar 12 2011

a(n) = (10^(n+3) - 3*9^(n+3) + 3*8^(n+3) - 7^(n+3))/6. - Bruno Berselli, Mar 12 2011

a(n) = 34*a(n-1) - 431*a(n-2) + 2414*a(n-3) - 5040*a(n-4); a(0)=1, a(1)=34, a(2)=725, a(3)=12410. - Harvey P. Dale, Jan 26 2012

Mathematica

CoefficientList[Series[1/((1-7x)(1-8x)(1-9x)(1-10x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{34, -431, 2414, -5040}, {1, 34, 725, 12410}, 21] (* Harvey P. Dale, Jan 26 2012 *)

Crossrefs

Sequence in context: A188711 A296334 A296634 * A028211 A028207 A028193

Adjacent sequences: A016106 A016107 A016108 * A016110 A016111 A016112

Keyword

nonn

Author

Robert G. Wilson v

Extensions

Offset changed to 0 by Vincenzo Librandi, Mar 12 2011

Status

approved