The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)