OFFSET
0,3
COMMENTS
For n >= 1, a(n) is equal to the number of functions f:{1,2,3,4,5}->{1,2,...,n} such that for a fixed x in {1,2,3,4,5} and a fixed y in {1,2,...,n} we have f(x) <> y. - Aleksandar M. Janjic and Milan Janjic, Mar 13 2007
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
G.f.: 2*x^2*(x^3 + 18*x^2 + 33*x + 8)/(x-1)^6. - Colin Barker, Nov 06 2012
Sum_{n>=2} 1/a(n) = 4 - zeta(2) - zeta(3) - zeta(4). - Amiram Eldar, Jul 05 2020
Product_{n>=2} (1 - 1/a(n)) = A146492. - Amiram Eldar, Nov 22 2022
MAPLE
a:=n->sum(sum(n^3, j=1..n), k=2..n): seq(a(n), n=0..31); # Zerinvary Lajos, May 09 2007
MATHEMATICA
Table[n^5 - n^4, {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 16, 162, 768, 2500}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *)
PROG
(Magma) [n^5-n^4: n in [0..50]]; // Vincenzo Librandi, Feb 12 2012
(PARI) a(n)=n^5-n^4 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 05 2003
STATUS
approved