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%I #9 Jul 23 2014 19:14:13
%S 1,1,4,27,256,3125,46656,823543,16777216,387420480,9999999100,
%T 285311610111,8916096934416,302874913851133,11111996418957812,
%U 437893325100944175,18446712799609551616,827238486905202346257,39346304291930549899764,1978413388840508514186871
%N Number of endofunctions on [n] such that no element has a preimage of cardinality nine.
%H Alois P. Heinz, <a href="/A245413/b245413.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = n! * [x^n] (exp(x)-x^9/9!)^n.
%p b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
%p `if`(i<1, 0, add(`if`(j=9, 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^9/9!)^n,{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Jul 23 2014 *)
%Y Column k=9 of A245405.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Jul 21 2014
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