OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).
FORMULA
a(n) = 18*6^n-45*5^n+48*4^n-27*3^n+8*2^n-1.
G.f.: -x*(720*x^5-1764*x^4+1408*x^3-585*x^2+110*x-9) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - Colin Barker, Feb 22 2015
EXAMPLE
a(8) = 15625591.
MAPLE
f:=n->18*6^n-45*5^n+48*4^n-27*3^n+8*2^n-1;
MATHEMATICA
LinearRecurrence[{21, -175, 735, -1624, 1764, -720}, {9, 79, 669, 5431, 42189, 314119}, 20] (* James C. McMahon, Dec 26 2024 *)
PROG
(PARI) Vec(-x*(720*x^5-1764*x^4+1408*x^3-585*x^2+110*x-9) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)) + O(x^100)) \\ Colin Barker, Feb 22 2015
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Aleksandar M. Janjic and Milan Janjic, Feb 08 2007
STATUS
approved