OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (38,-539,3382,-7920)
FORMULA
If we define f(m,j,x)=sum(binomial(m,k)*stirling2(k,j)*x^(m-k),k=j..m) then a(n-3)=f(n,3,8), (n>=3). - Milan Janjic, Apr 26 2009
a(n) = 38*a(n-1) - 539*a(n-2) + 3382*a(n-3) - 7920*a(n-4), n>=4. - Vincenzo Librandi, Mar 17 2011
a(n) = 21*a(n-1) - 110*a(n-2) + 9^(n+1) - 8^(n+1), n>=2. - Vincenzo Librandi, Mar 17 2011
a(n) = 11^(n+3)/6 -5*10^(n+2) -4*8^(n+2)/3 + 9^(n+3)/2. - R. J. Mathar, Mar 18 2011
MATHEMATICA
CoefficientList[Series[1/((1-8*x)*(1-9*x)*(1-10*x)*(1-11*x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 23 2013 *)
PROG
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-8*x)*(1-9*x)*(1-10*x)*(1-11*x)))); /* or */ I:=[1, 38, 905, 17290]; [n le 4 select I[n] else 38*Self(n-1)-539*Self(n-2)+3382*Self(n-3)-7920*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Jun 24 2013
(PARI) x='x+O('x^30); Vec(1/((1-8*x)*(1-9*x)*(1-10*x)*(1-11*x))) \\ G. C. Greubel, Feb 07 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved