OFFSET
0,2
COMMENTS
A row of A099239.
Equals INVERT transform of A000389, C(n,5). [Gary W. Adamson, Feb 02 2009]
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
D. Birmajer, J. B. Gil, and M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3, example 16.
Index entries for linear recurrences with constant coefficients, signature (7,-15,20,-15,6,-1).
FORMULA
G.f.: 1/((1-x)^6-x).
a(n) = 7*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
a(n) = Sum_{k=0..n} binomial(6*n-5*(k-1), k).
a(n) = Sum_{k=0..n} binomial(n+5*(k+1), k+5*(k+1)).
a(n) = Sum_{k=0..n} binomial(n+5*(k+1), n-k).
MATHEMATICA
CoefficientList[Series[1/((1 - x)^6 - x), {x, 0, 50}], x] (* G. C. Greubel, Nov 24 2017 *)
LinearRecurrence[{7, -15, 20, -15, 6, -1}, {1, 7, 34, 153, 686, 3088}, 30] (* Harvey P. Dale, May 06 2018 *)
PROG
(PARI) my(x='x+O('x^50)); Vec(1/((1-x)^6-x)) \\ G. C. Greubel, Nov 24 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 08 2004
STATUS
approved