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

0,3

Links

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

Formula

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

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 *)

Crossrefs

Column k=9 of A245405.

Sequence in context: A324807 A245412 A324808 * A344658 A226272 A086756

Adjacent sequences: A245410 A245411 A245412 * A245414 A245415 A245416

Keyword

nonn

Author

Alois P. Heinz, Jul 21 2014

Status

approved