A245412 Number of endofunctions on [n] such that no element has a preimage of cardinality eight.

1, 1, 4, 27, 256, 3125, 46656, 823543, 16777208, 387419841, 9999963550, 285309855611, 8916013480716, 302870943384061, 11111803896854038, 437883715342385775, 18446216323273596016, 827211862188632409057, 39344820189873938423748, 1978327362506349226513213

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^8/8!)^n.

Maple

b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
      `if`(i<1, 0, add(`if`(j=8, 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^8/8!)^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 23 2014 *)

Crossrefs

Column k=8 of A245405.

Sequence in context: A324806 A245411 A324807 * A324808 A245413 A344658

Adjacent sequences: A245409 A245410 A245411 * A245413 A245414 A245415

Keyword

nonn

Author

Alois P. Heinz, Jul 21 2014

Status

approved