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Number of functions f:{1,2,...,n}->{1,2,...,n} such that Im(f) contains 5 fixed elements.
1

%I #7 Dec 24 2012 02:05:31

%S 120,2520,52080,1164240,28594440,771309000,22746757440,729419296320,

%T 25295774463960,943934414262840,37728367833920400,1608541146018621360,

%U 72881990543360522280,3497670707401587171240,177254235519701336515680

%N Number of functions f:{1,2,...,n}->{1,2,...,n} such that Im(f) contains 5 fixed elements.

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>

%F a(n)=n^n-5*(n-1)^n+10*(n-2)^n-10*(n-3)^n+5*(n-4)^n-(n-5)^n.

%e a(10)=771309000.

%p a(n):n->n^n-5*(n-1)^n+10*(n-2)^n-10*(n-3)^n+5*(n-4)^n-(n-5)^n;

%t Drop[Table[Sum[(-1)^k Binomial[5,k] (n-k)^n,{k,0,5}],{n,1,20}],4] (* _Geoffrey Critzer_, Dec 23 2012 *)

%Y Cf. A126781, A126780, A126779, A126778.

%K nonn

%O 5,1

%A Aleksandar M. Janjic and _Milan Janjic_, Mar 08 2007