A201996 The number of endofunctions on n points such that all recurrent elements have at most 3 preimages and all nonrecurrent elements have at most 2 preimages.
1, 1, 4, 27, 252, 3000, 43380, 737730, 14419440, 318381840, 7835486400, 212634298800, 6307073942400, 202983948367200, 7044249755743200, 262198957638618000, 10419369722457696000, 440257835691561888000, 19709455059507717504000, 931885122471464345184000, 46401644730376725229440000
Offset: 0
Keywords
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..390
- Giulio Cerbai and Anders Claesson, Counting fixed-point-free Cayley permutations, arXiv:2507.09304 [math.CO], 2025. See p. 25.
Programs
-
Mathematica
a = (1 - x - (1 - 2 x - x^2)^(1/2))/x; Range[0, 20]! CoefficientList[Series[1/(1 - a), {x, 0, 20}], x]
Formula
E.g.f.: 1/(1-A(x)) where A(x) is the e.g.f. for A036774.
a(n) ~ n! * (5/2)^n/5. - Vaclav Kotesovec, Sep 24 2013