cp's OEIS Frontend

A239768 Number of pairs of functions (f,g) from a set of n elements into itself satisfying f(x) = f(g(f(x))).

%I A239768 #44 Jun 13 2022 11:05:40
%S A239768 1,1,10,195,6808,362745,26848656,2621263519,324981308800,
%T A239768 49669569764433,9146879704748800,1993011341241988551,
%U A239768 506190915590699695104,148000190814308473203433,49289886405448749446514688,18529196186934893511062427375,7800708229072237749055062900736,3652486190893312491910941333813537
%N A239768 Number of pairs of functions (f,g) from a set of n elements into itself satisfying f(x) = f(g(f(x))).
%H A239768 Alois P. Heinz, <a href="/A239768/b239768.txt">Table of n, a(n) for n = 0..251</a>
%F A239768 a(n) = Sum_{k=0..n} (n!/(n-k)!) * C(n,k) * (n*k)^(n-k). - _David Einstein_, Oct 10 2016
%t A239768 A[n_] := If[n == 0, 1, Sum[(n!/(n - k)!) Binomial[n, k] (n k)^(n - k), {k, 1, n}]]
%t A239768 Table[A[n],{n,10}] (* _David Einstein_, Oct 10 2016 *)
%o A239768 (PARI) a(n) = sum(k= 0, n, (n!/(n-k)!)*binomial(n,k)*(n*k)^(n-k)); \\ _Michel Marcus_, Oct 11 2016; corrected Jun 13 2022
%Y A239768 Cf. A181162.
%K A239768 nonn
%O A239768 0,3
%A A239768 _Chad Brewbaker_, Mar 26 2014
%E A239768 a(6)-a(7) from _Giovanni Resta_, Mar 28 2014
%E A239768 a(8)-a(17) from _David Einstein_, Oct 10 2016