A245408 - OEIS

%I #9 Jul 23 2014 19:04:40

%S 1,1,4,27,252,3025,44406,770623,15434616,350420337,8893045900,

%T 249474767861,7665670072116,256045368531433,9237038259841770,

%U 357934480164387225,14827066792663179616,653843231295154192017,30581468519362170893784,1512123060477719223218791

%N Number of endofunctions on [n] such that no element has a preimage of cardinality four.

%H Alois P. Heinz, <a href="/A245408/b245408.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = n! * [x^n] (exp(x)-x^4/4!)^n.

%p b:= proc(n, i) option remember; `if`(n=0 and i=0, 1, `if`(i<1, 0,

%p        add(`if`(j=4, 0, b(n-j, i-1) *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^4/4!)^n,{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Jul 23 2014 *)

%Y Column k=4 of A245405.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jul 21 2014