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A245414 Number of endofunctions on [n] such that no element has a preimage of cardinality ten. 2
1, 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 9999999990, 285311669401, 8916100352424, 302875100167549, 11112006425304162, 437893866154577295, 18446742614251551616, 827240173137280043281, 39346402580883043716420, 1978419307503657602437003 (list; graph; refs; listen; history; text; internal format)
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: A117280 A067040 A070271 * A000312 A177885 A086783

Adjacent sequences:  A245411 A245412 A245413 * A245415 A245416 A245417

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 21 2014

STATUS

approved

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Last modified October 22 05:06 EDT 2018. Contains 316432 sequences. (Running on oeis4.)