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A212559 Number of functions f:{1,2,...,n}->{1,2,...,n} such that every non-recurrent 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 (list; graph; refs; listen; history; text; internal format)
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 k-th iteration of functional composition.

The functional digraphs are composed of cycles of rooted trees with every non-root vertex of degree 1 or 2. Cf. A006152.

LINKS

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

FORMULA

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

MATHEMATICA

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

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Last modified March 21 10:13 EDT 2019. Contains 321368 sequences. (Running on oeis4.)