OFFSET
0,2
LINKS
Matthew House, Table of n, a(n) for n = 0..1040
Index entries for linear recurrences with constant coefficients, signature (30,-335,1650,-3024).
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,3,6), (n >= 3). [Milan Janjic, Apr 26 2009]
a(n) = 17*a(n-1) - 72*a(n-2) + 7^(n+1) - 6^(n+1), a(0)=1, a(1)=30. - Vincenzo Librandi, Mar 11 2011
a(n) = (9^(n+3) - 3*8^(n+3) + 3*7^(n+3) - 6^(n+3))/6. [Yahia Kahloune, Jun 12 2013]
a(n) = 30*a(n-1) - 335*a(n-2) + 1650*a(n-3) - 3024*a(n-4). - Matthew House, Feb 11 2017
MATHEMATICA
CoefficientList[Series[ 1/((1-6x)(1-7x)(1-8x)(1-9x)), {x, 0, 20} ], x]
LinearRecurrence[{30, -335, 1650, -3024}, {1, 30, 565, 8550}, 20] (* Harvey P. Dale, Mar 27 2023 *)
PROG
(PARI) Vec(1/((1-6*x)*(1-7*x)*(1-8*x)*(1-9*x)) + O(x^30)) \\ Michel Marcus, Feb 12 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved