OFFSET
0,4
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1)
FORMULA
a(n) = binomial(n + 5, 5) - 4*binomial(n + 2, 2) - 3*binomial(n + 1, 1) + 12*binomial(n, 0) - 6*binomial(n - 1, -1).
G.f.: - y^3*( - 24*y^2 - 16 + 33*y + 6*y^3)/( - 1 + y)^6.
E.g.f. for ordered k-block bicoverings of an unlabeled n-set is: exp( - x - x^2/2*y/(1 - y))*Sum_{k>=0} 1/(1 - y)^binomial(k, 2)*x^k/k!.
a(n) = (n+5)*(n-1)*(n-2)*(n^2+13*n+72)/120, n>0. - R. J. Mathar, Aug 15 2017
PROG
(PARI) a(n) = if(n<1, 0, binomial(n + 5, 5) - 4*binomial(n + 2, 2) - 3*binomial(n + 1, 1) + 12*binomial(n, 0) - 6*binomial(n - 1, -1)) \\ Harry J. Smith, Jul 01 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Feb 26 2001
STATUS
approved