A245409 Number of endofunctions on [n] such that no element has a preimage of cardinality five.

1, 1, 4, 27, 256, 3120, 46476, 818251, 16623552, 382775625, 9851207860, 280231042751, 8731004146272, 295688565207373, 10815259910601524, 424893916814719815, 17844053214957081856, 797744088027002799121, 37826128915102284480144, 1896083271482048297688979

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^5/5!)^n.

Maple

b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
      `if`(i<1, 0, add(`if`(j=5, 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^5/5!)^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 23 2014 *)

Crossrefs

Column k=5 of A245405.

Sequence in context: A239491 A365095 A324804 * A190125 A324805 A245410

Adjacent sequences: A245406 A245407 A245408 * A245410 A245411 A245412

Keyword

nonn

Author

Alois P. Heinz, Jul 21 2014

Status

approved