A245410 Number of endofunctions on [n] such that no element has a preimage of cardinality six.

1, 1, 4, 27, 256, 3125, 46650, 823249, 16766240, 387033417, 9986221900, 284803470611, 8896457440872, 302075780925685, 11077712976422470, 436342859278138275, 18372866764869817216, 823539597176786793105, 39151767720093507173304, 1967688517596911564272795

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^6/6!)^n.

Maple

b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
      `if`(i<1, 0, add(`if`(j=6, 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^6/6!)^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 23 2014 *)

Crossrefs

Column k=6 of A245405.

Sequence in context: A245409 A190125 A324805 * A324806 A245411 A324807

Adjacent sequences: A245407 A245408 A245409 * A245411 A245412 A245413

Keyword

nonn

Author

Alois P. Heinz, Jul 21 2014

Status

approved