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%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
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