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Number of endofunctions on [n] such that no element has a preimage of cardinality seven.
2

%I #9 Jul 23 2014 19:13:15

%S 1,1,4,27,256,3125,46656,823536,16776768,387399753,9999125200,

%T 285275370611,8914569819552,302808495261181,11108991885125512,

%U 437751439912499175,18439707410896028416,826876746821203814161,39326776141693679404128,1977312147376328609765419

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

%H Alois P. Heinz, <a href="/A245411/b245411.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = n! * [x^n] (exp(x)-x^7/7!)^n.

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

%p `if`(i<1, 0, add(`if`(j=7, 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^7/7!)^n,{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Jul 23 2014 *)

%Y Column k=7 of A245405.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jul 21 2014