The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A235328 Number of ordered pairs of endofunctions (f,g) on a set of n elements satisfying f(x) = g(f(f(x))). 8
 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 log(a(n)) ~ log(sqrt(2*Pi) * n^(2*n - n/LambertW(exp(1)*n) + 1/2) / (LambertW(exp(1)*n) * exp(n/LambertW(exp(1)*n)) * (LambertW(exp(1)*n) - 1)^(n*(1 - 1/LambertW(exp(1)*n))))). - Vaclav Kotesovec, Feb 20 2022 More precise asymptotics: a(n) ~ sqrt(2*Pi) * (w^2 - w - 1 + 2/w) * exp(n*(1/w^3 - 1/w)) * n^(2*n + n/w^3 - n/w + 1/2) * (w^2 - 1)^(n*(1 + 1/w^3 - 1/w)) * (1 - w^2 + w^3)^(n/w - n - n/w^3 - 1), where w = LambertW(exp(1)*n). - Vaclav Kotesovec, Feb 23 2022 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, A351795. Sequence in context: A364982 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

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

Last modified October 4 20:53 EDT 2023. Contains 365888 sequences. (Running on oeis4.)