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%I #9 Jul 23 2014 19:12:02
%S 1,1,4,27,256,3120,46476,818251,16623552,382775625,9851207860,
%T 280231042751,8731004146272,295688565207373,10815259910601524,
%U 424893916814719815,17844053214957081856,797744088027002799121,37826128915102284480144,1896083271482048297688979
%N Number of endofunctions on [n] such that no element has a preimage of cardinality five.
%H Alois P. Heinz, <a href="/A245409/b245409.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = n! * [x^n] (exp(x)-x^5/5!)^n.
%p b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
%p `if`(i<1, 0, add(`if`(j=5, 0, b(n-j, i-1)*
%p binomial(n, j)), j=0..n)))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..25);
%t Table[n!*SeriesCoefficient[(E^x-x^5/5!)^n,{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Jul 23 2014 *)
%Y Column k=5 of A245405.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Jul 21 2014
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