OFFSET
1,1
COMMENTS
Note that the first seven terms of the sequence are powers of 9.
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 (36,-546,4536,-22449,67284,-118124,109584,-40320).
FORMULA
a(n) = 8*8^n-28*7^n+56*6^n-70*5^n+56*4^n-28*3^n+8*2^n-1.
G.f.: -9*x*(4480*x^7 -12176*x^6 +11772*x^5 -6168*x^4 +1809*x^3 -303*x^2 +27*x -1)/((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)). - Colin Barker, Feb 22 2015
EXAMPLE
a(5) = 59049.
MAPLE
f:=n->8*8^n-28*7^n+56*6^n-70*5^n+56*4^n-28*3^n+8*2^n-1;
MATHEMATICA
Table[8*8^n-28*7^n+56*6^n-70*5^n+56*4^n-28*3^n+8*2^n-1, {n, 20}] (* James C. McMahon, Dec 20 2024 *)
PROG
(PARI) Vec(-9*x*(4480*x^7-12176*x^6+11772*x^5-6168*x^4+1809*x^3-303*x^2+27*x-1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)) + O(x^100)) \\ Colin Barker, Feb 22 2015
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Aleksandar M. Janjic and Milan Janjic, Jan 28 2007, Feb 13 2007
STATUS
approved