%I #31 Sep 08 2022 08:45:11
%S 0,0,32,486,3072,12500,38880,100842,229376,472392,900000,1610510,
%T 2737152,4455516,6991712,10631250,15728640,22717712,32122656,44569782,
%U 60800000,81682020,108226272,141599546,183140352,234375000,297034400,373071582,464679936
%N a(n) = n^6 - n^5.
%C For n>=1, a(n) is equal to the number of functions f:{1,2,3,4,5,6}->{1,2,...,n} such that for a fixed x in {1,2,3,4,5,6} and a fixed y in {1,2,...,n} we have f(x)<>y. - Aleksandar M. Janjic and _Milan Janjic_, Mar 13 2007
%H Vincenzo Librandi, <a href="/A085539/b085539.txt">Table of n, a(n) for n = 0..1000</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: -2*x^2*(x^4+41*x^3+171*x^2+131*x+16)/(x-1)^7. - _Colin Barker_, Nov 06 2012
%F Sum_{n>=2} 1/a(n) = 5 - Sum_{k=2..5} zeta(k). - _Amiram Eldar_, Jul 05 2020
%t f[n_]:=n^6-n^5;f[Range[0,60]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 10 2011 *)
%t Table[n^6 - n^5, {n, 0, 50}] (* _Vincenzo Librandi_, Aug 15 2016 *)
%o (PARI) a(n)=n^6-n^5 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Magma) [n^6-n^5: n in [0..40]]; // _Vincenzo Librandi_, Aug 15 2016
%Y A diagonal of A228273.
%Y Cf. A000584, A001014.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Jul 05 2003