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A215720 The number of functions f:{1,2,...,n}->{1,2,...,n}, endofunctions, such that exactly one nonrecurrent element is mapped into each recurrent element. 1
1, 0, 2, 6, 60, 560, 7350, 111552, 2009672, 41378976, 963527850, 25009038560, 716437784172, 22453784964624, 764345507271710, 28085186967504240, 1107971902218683280, 46710909213378892352, 2095883952368863510098, 99724281567446320231104, 5015524096516005263567540 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

x in {1,2,...,n} is a recurrent element if there is some k such that f^k(x) = x where f^k(x) denotes iterated functional composition.  In other words, a recurrent element is in a cycle of the functional digraph.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..150

FORMULA

E.g.f.: 1/(1 - x*T(x)) where T(x) is the e.g.f. for A000169.

a(n) = n! * Sum_{i=0..floor(n/2)} i*(n-i)^(n-2*i-1)/(n-2*i)! for n>0, a(0) = 1. - Alois P. Heinz, Aug 22 2012

a(n) ~ exp(1)/(exp(1)-1)^2 * n^(n-1). - Vaclav Kotesovec, Sep 30 2013

EXAMPLE

a(2) = 2 because we have: (1->1,2->1), (1->2,2->2).

MAPLE

a:= n-> `if`(n=0, 1, n! *add(i*(n-i)^(n-2*i-1)/(n-2*i)!, i=0..n/2)):

seq(a(n), n=0..30);  # Alois P. Heinz, Aug 22 2012

MATHEMATICA

nn = 20; t = Sum[n^(n - 1) x^n/n!, {n, 1, nn}];

Range[0, nn]! CoefficientList[Series[1/(1 - x t) , {x, 0, nn}], x]

CROSSREFS

Cf. A055541, A195203, A098875.

Sequence in context: A226959 A083135 A056604 * A211936 A156972 A086332

Adjacent sequences:  A215717 A215718 A215719 * A215721 A215722 A215723

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Aug 22 2012

STATUS

approved

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Last modified April 8 01:57 EDT 2020. Contains 333312 sequences. (Running on oeis4.)