A239759 Number of pairs of functions (f,g) from a set of n elements into itself satisfying f(g(x)) = g(f(g(x))).

1, 1, 8, 147, 5032, 274765, 21702096, 2327543743, 324317092352, 56816985879801, 12201268360672000, 3147485927264980411, 959356469360927222784, 340785570064053310187173, 139449094593887763170361344, 65080820095941557895304404375

Offset: 0

Author

Chad Brewbaker, Mar 26 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..241

Crossrefs

Cf. A000248, A000949.

Programs

Mathematica

Unprotect[Power]; 0^0 = 1;
a[n_] := If[n == 0, 1, Sum[Binomial[n, k] k^k Sum[Binomial[n - k, j] k^j (j + k - 1)^j ((n - k)(j + k))^(n - j - k), {j, 0, n - k}], {k, 1, n}]];
a /@ Range[0, 15] (* Jean-François Alcover, Oct 04 2019 *)

PARI

a(n) = if(n==0,1,sum(k=1,n, binomial(n,k) * k^k * (sum(j=0,n-k, binomial(n-k,j)*k^j*(j+k-1)^j*((n-k)*(j+k))^(n-j-k))))) \\ Joerg Arndt, Oct 13 2016

Formula

a(n) = Sum_{k=0..n} C(n,k) * k^k * (Sum_{j=0..n-k} C(n-k,j)*k^j*(j+k-1)^j*((n-k)*(j+k))^(n-j-k)). - David Einstein, Oct 11 2016

Extensions

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

a(8)-a(15) from David Einstein, Oct 11 2016