A245414 - OEIS

%I #9 Jul 23 2014 19:14:50

%S 1,1,4,27,256,3125,46656,823543,16777216,387420489,9999999990,

%T 285311669401,8916100352424,302875100167549,11112006425304162,

%U 437893866154577295,18446742614251551616,827240173137280043281,39346402580883043716420,1978419307503657602437003

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

%H Alois P. Heinz, <a href="/A245414/b245414.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = n! * [x^n] (exp(x)-x^10/10!)^n.

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

%p       `if`(i<1, 0, add(`if`(j=10, 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^10/10!)^n,{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Jul 23 2014 *)

%Y Column k=10 of A245405.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jul 21 2014