OFFSET
0,2
COMMENTS
This gives the fourth column of the Sheffer triangle A143495 (3-restricted Stirling2 numbers). See the e.g.f. given below, and comments on the general case under A193685. - Wolfdieter Lang, Oct 08 2011
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (18,-119,342,-360).
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,3,3), (n >= 3). - Milan Janjic, Apr 26 2009
a(n) = -5^(n+3)/2 + 2*4^(n+2)+ 6^(n+2) - 3^(n+2)/2. - R. J. Mathar, Mar 22 2011
O.g.f.: 1/((1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)).
E.g.f.: (d^3/dx^3)(exp(3*x)*((exp(x)-1)^3)/3!). - Wolfdieter Lang, Oct 08 2011
MATHEMATICA
CoefficientList[Series[1/((1-3x)(1-4x)(1-5x)(1-6x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{18, -119, 342, -360}, {1, 18, 205, 1890}, 30] (* Harvey P. Dale, Jan 29 2024 *)
PROG
(PARI) Vec(1/((1-3*x)*(1-4*x)*(1-5*x)*(1-6*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved