

A212559


Number of functions f:{1,2,...,n}>{1,2,...,n} such that every nonrecurrent element has at most one preimage.


0



1, 1, 4, 27, 244, 2745, 36966, 580111, 10399096, 209672721, 4696872490, 115732052271, 3110867569140, 90587751885241, 2840805169411678, 95450112571474095, 3420897993621996016, 130266500391456691233, 5252293203395848789842, 223535386151669737094095, 10014286301754519472897900
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OFFSET

0,3


COMMENTS

An element x of {1,2,...,n} is a recurrent element if there exists a positive integer k such that (f^k)(x) = x where f^k is the kth iteration of functional composition.
The functional digraphs are composed of cycles of rooted trees with every nonroot vertex of degree 1 or 2. Cf. A006152.


LINKS

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


FORMULA

E.g.f.: 1/(1A(x)) where A(x) is the e.g.f. for A006152.


MATHEMATICA

nn=20; a=x Exp[x/(1x)]; Range[0, nn]! CoefficientList[Series[1/(1a), {x, 0, nn}], x]


CROSSREFS

Sequence in context: A303559 A161120 A183430 * A265268 A121063 A229619
Adjacent sequences: A212556 A212557 A212558 * A212560 A212561 A212562


KEYWORD

nonn


AUTHOR

Geoffrey Critzer, May 21 2012


STATUS

approved



