A245411 Number of endofunctions on [n] such that no element has a preimage of cardinality seven.

1, 1, 4, 27, 256, 3125, 46656, 823536, 16776768, 387399753, 9999125200, 285275370611, 8914569819552, 302808495261181, 11108991885125512, 437751439912499175, 18439707410896028416, 826876746821203814161, 39326776141693679404128, 1977312147376328609765419

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^7/7!)^n.

Maple

b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
      `if`(i<1, 0, add(`if`(j=7, 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^7/7!)^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 23 2014 *)

Crossrefs

Column k=7 of A245405.

Sequence in context: A324805 A245410 A324806 * A324807 A245412 A324808

Adjacent sequences: A245408 A245409 A245410 * A245412 A245413 A245414

Keyword

nonn

Author

Alois P. Heinz, Jul 21 2014

Status

approved