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A204042 The number of functions f:{1,2,...,n}->{1,2,...,n} (endofunctions) such that all of the fixed points in f are isolated. 0
1, 1, 2, 12, 120, 1520, 23160, 413952, 8505280, 197631072, 5125527360, 146787894440, 4601174623584, 156693888150384, 5761055539858528, 227438694372072120, 9596077520725211520, 430920897407809702208, 20520683482765477749120, 1032920864149903149579336, 54797532208320308334631840 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Note this sequence counts the functions enumerated by A065440 for which the statement is vacuously true.

a(n) is also the number of partial endofunctions on {1,2,...,n} without fixed points.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

E.g.f.: exp(x)*A(x) where A(x) is the e.g.f. for A065440.

a(n) ~ exp(exp(-1)-1)*n^n. - Vaclav Kotesovec, Sep 24 2013

EXAMPLE

a(2)=2 because there are two functions f:{1,2}->{1,2} in which all the fixed points are isolated: 1->1,2->2  and 1->2,2->1 (which has no fixed points).

MATHEMATICA

t = Sum[n^(n-1) x^n/n!, {n, 1, 20}]; Range[0, 20]! CoefficientList[Series[Exp[x] Exp[Log[1/(1-t)]-t], {x, 0, 20}], x]

CROSSREFS

Sequence in context: A003580 A052580 A134095 * A302702 A189981 A326000

Adjacent sequences:  A204039 A204040 A204041 * A204043 A204044 A204045

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jan 09 2012

STATUS

approved

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Last modified August 2 14:30 EDT 2021. Contains 346428 sequences. (Running on oeis4.)