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A235328 Number of ordered pairs of endofunctions (f,g) on a set of n elements satisfying f(x) = g(f(f(x))). 6
1, 1, 6, 69, 1336, 39145, 1598256, 85996561, 5872177536, 494848403793, 50333180780800, 6068500612311841, 854434117410352128, 138752719761249646585, 25714777079368557164544, 5389541081414619785888625, 1267387594395443339970052096, 332074775201035547446532113825 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This also counts pairs (f,g) satisfying f(x) = g(f^{r}(x)) for r > 1. - David Einstein, Nov 18 2016

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..263

FORMULA

a(n) = Sum_{k=1..n} k! * C(n, k) * (n*k)^(n-k). - David Einstein, Oct 10 2016

a(n) = n! * [x^n] 1/(1 - x*exp(n*x)). - Ilya Gutkovskiy, Nov 26 2017

MAPLE

a:= proc(n) option remember; local b; b:=

      proc(m, i) option remember; `if`(m=0, n^i, `if`(i<1, 0,

        add(b(m-j, i-1)*binomial(m, j)*j, j=0..m)))

      end: forget(b):

      b(n$2)

    end:

seq(a(n), n=0..20);  # Alois P. Heinz, Jul 23 2014

MATHEMATICA

a[n_] := If[n==0, 1, Sum[k! Binomial[n, k] (n k)^(n - k), {k, 1, n}]]

  Table[a[n], {n, 20}] (* David Einstein, Oct 10 2016 *)

CROSSREFS

Cf. A000248, A000949, A181162.

Sequence in context: A235327 A098639 A305110 * A296783 A218683 A188406

Adjacent sequences:  A235325 A235326 A235327 * A235329 A235330 A235331

KEYWORD

nonn

AUTHOR

Chad Brewbaker, Mar 26 2014

EXTENSIONS

a(6)-a(7) from Giovanni Resta, Mar 26 2014

a(8)-a(17) from Alois P. Heinz, Jul 23 2014

STATUS

approved

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Last modified August 13 02:52 EDT 2020. Contains 336441 sequences. (Running on oeis4.)