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%I #14 Jan 10 2019 22:52:48
%S 6,60,750,11340,201726,4131036,95750430,2478397020,70864914846,
%T 2218385781612,75463626886830,2771883228523500,109340261175108606,
%U 4609962410815813308,206883575626027168830,9846362287666897852860
%N Number of functions f:{1,2,...,n}->{1,2,...,n} such that Im(f) contains 3 fixed elements.
%H Robert Israel, <a href="/A126779/b126779.txt">Table of n, a(n) for n = 3..386</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%F a(n) = n^n-3*(n-1)^n+3*(n-2)^n-(n-3)^n, (n=3,4,...)
%F E.g.f.: (W(-x)^3 + 3*x*W(-x)^2 + 3*x^2*W(-x) + x^3)/(W(-x)^3*(1 + W(-x))) where W is the Lambert W function. - _Robert Israel_, Jan 10 2019
%e a(7)=201726
%p a:=n->n^n-3*(n-1)^n+3*(n-2)^n-(n-3)^n;
%t Drop[Table[Sum[(-1)^k Binomial[3,k] (n-k)^n,{k,0,3}],{n,1,20}],2] (* _Geoffrey Critzer_, Dec 23 2012 *)
%K nonn
%O 3,1
%A Aleksandar M. Janjic and _Milan Janjic_, Feb 18 2007
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