A245414 Number of endofunctions on [n] such that no element has a preimage of cardinality ten.

1, 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 9999999990, 285311669401, 8916100352424, 302875100167549, 11112006425304162, 437893866154577295, 18446742614251551616, 827240173137280043281, 39346402580883043716420, 1978419307503657602437003

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^10/10!)^n.

Maple

b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
      `if`(i<1, 0, add(`if`(j=10, 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^10/10!)^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 23 2014 *)

Crossrefs

Column k=10 of A245405.

Sequence in context: A067040 A070271 A324809 * A177885 A000312 A086783

Adjacent sequences: A245411 A245412 A245413 * A245415 A245416 A245417

Keyword

nonn

Author

Alois P. Heinz, Jul 21 2014

Status

approved