A245413 Number of endofunctions on [n] such that no element has a preimage of cardinality nine.

1, 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420480, 9999999100, 285311610111, 8916096934416, 302874913851133, 11111996418957812, 437893325100944175, 18446712799609551616, 827238486905202346257, 39346304291930549899764, 1978413388840508514186871

Offset: 0

Author

Alois P. Heinz, Jul 21 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Column k=9 of A245405.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
      `if`(i<1, 0, add(`if`(j=9, 0, b(n-j, i-1)*
       binomial(n, j)), j=0..n)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);

Mathematica

Table[n!*SeriesCoefficient[(E^x-x^9/9!)^n,{x,0,n}],{n,0,20}] (* Vaclav Kotesovec, Jul 23 2014 *)

Formula

a(n) = n! * [x^n] (exp(x)-x^9/9!)^n.