cp's OEIS Frontend

A239750 Number of ordered pairs of endofunctions (f,g) on a set of n elements satisfying g(f(x)) = f(f(f(x))).

%I A239750 #39 Oct 03 2019 11:19:35
%S A239750 1,1,6,87,2200,84245,4492656,315937195,28186856832,3099006365769,
%T A239750 410478164588800,64323095036300111,11748771067445148672,
%U A239750 2470422069374379054493,591735532838657160296448,160004357420756572368889875,48458574881000820765562863616
%N A239750 Number of ordered pairs of endofunctions (f,g) on a set of n elements satisfying g(f(x)) = f(f(f(x))).
%C A239750 As observed by _Yuval Filmus_, this also counts pairs (f,g) that satisfy g(f(x)) = f^{k}(x) for k >= 1. - _Chad Brewbaker_, Mar 27 2014
%H A239750 Alois P. Heinz, <a href="/A239750/b239750.txt">Table of n, a(n) for n = 0..200</a>
%H A239750 Yuval Filmus, <a href="http://cstheory.stackexchange.com/q/21764">Answer to 'A curious Wilf equivalence class of function compositions'</a>, Mar 27 2014
%F A239750 a(n) = Sum_{k=0..n} C(n,k) * k^n * (n-1)^(n-k) = Sum_{k=0..n} C(n,k) * A048993(n,k) * k! * n^(n-k). - _Alois P. Heinz_, Jul 23 2014
%p A239750 a:= n-> add(binomial(n, k)*k^n*(n-1)^(n-k), k=0..n):
%p A239750 seq(a(n), n=0..20);  # _Alois P. Heinz_, Jul 23 2014
%t A239750 a[n_] := If[n<2, 1, Sum[Binomial[n, k]*k^n*(n-1)^(n-k), {k, 0, n}]];
%t A239750 a /@ Range[0, 20] (* _Jean-François Alcover_, Oct 03 2019, after _Alois P. Heinz_ *)
%Y A239750 Cf. A000248, A000949, A048993, A181162, A241015.
%Y A239750 Column k=1 of A245980.
%K A239750 nonn
%O A239750 0,3
%A A239750 _Chad Brewbaker_, Mar 26 2014
%E A239750 a(6)-a(7) from _Giovanni Resta_, Mar 26 2014
%E A239750 a(8)-a(16) from _Alois P. Heinz_, Jul 17 2014