|
%I #9 Jul 23 2014 19:13:42
%S 1,1,4,27,256,3125,46656,823543,16777208,387419841,9999963550,
%T 285309855611,8916013480716,302870943384061,11111803896854038,
%U 437883715342385775,18446216323273596016,827211862188632409057,39344820189873938423748,1978327362506349226513213
%N Number of endofunctions on [n] such that no element has a preimage of cardinality eight.
%H Alois P. Heinz, <a href="/A245412/b245412.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = n! * [x^n] (exp(x)-x^8/8!)^n.
%p b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
%p `if`(i<1, 0, add(`if`(j=8, 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^8/8!)^n,{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Jul 23 2014 *)
%Y Column k=8 of A245405.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Jul 21 2014
|
