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

0,3

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 A036774.

a(n) ~ n! * (5/2)^n/5. - Vaclav Kotesovec, Sep 24 2013

Mathematica

a = (1 - x - (1 - 2 x - x^2)^(1/2))/x; Range[0, 20]! CoefficientList[Series[1/(1 - a), {x, 0, 20}], x]

Crossrefs

Sequence in context: A239373 A239377 A239371 * A239368 A245408 A243696

Adjacent sequences: A201993 A201994 A201995 * A201997 A201998 A201999

Keyword

nonn

Author

Geoffrey Critzer, Dec 07 2011

Status

approved