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

1, 1, 10, 195, 6808, 362745, 26848656, 2621263519, 324981308800, 49669569764433, 9146879704748800, 1993011341241988551, 506190915590699695104, 148000190814308473203433, 49289886405448749446514688, 18529196186934893511062427375, 7800708229072237749055062900736, 3652486190893312491910941333813537

Offset: 0

Author

Chad Brewbaker, Mar 26 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..251

Crossrefs

Cf. A181162.

Programs

Mathematica

A[n_] := If[n == 0, 1, Sum[(n!/(n - k)!) Binomial[n, k] (n k)^(n - k), {k, 1, n}]]
Table[A[n],{n,10}] (* David Einstein, Oct 10 2016 *)

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

Formula

a(n) = Sum_{k=0..n} (n!/(n-k)!) * C(n,k) * (n*k)^(n-k). - David Einstein, Oct 10 2016

Extensions

a(6)-a(7) from Giovanni Resta, Mar 28 2014

a(8)-a(17) from David Einstein, Oct 10 2016