A239781 - OEIS

%I #17 Feb 28 2017 22:55:03

%S 1,1,12,321,15280,1127745,118507536,16731979033,3044595017472,

%T 692050790547297,191796657547052800,63563842088104098081,

%U 24793529117087476242432,11232023076988690608825505,5843573099019743656060348416,3457799186387568447755745563625

%N Number of pairs of functions f, g from a size n set into itself satisfying f(g(x)) = f(f(g(x))).

%H Alois P. Heinz, <a href="/A239781/b239781.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = Sum_{k=0..n} C(n,k) * Sum_{i=0..n-k} C(n-k,i) * k^i * (n-k-1)^(n-k-i) * (k+i)^n. - _Alois P. Heinz_, Jul 17 2014

%p a:= n-> add(binomial(n, k)*add(binomial(n-k, i)*k^i*

%p         (n-k-1)^(n-k-i)*(k+i)^n, i=0..n-k), k=0..n):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Jul 17 2014

%t Unprotect[Power]; 0^0 = 1; a[n_] := Sum[Binomial[n, k]*Sum[Binomial[n-k, i]*k^i*(n-k-1)^(n-k-i)*(k+i)^n, {i, 0, n-k}], {k, 0, n}]; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Feb 28 2017, after _Alois P. Heinz_ *)

%Y Cf. A181162, A239769, A239773.

%Y Cf. A000248.

%K nonn

%O 0,3

%A _Chad Brewbaker_, Mar 26 2014

%E a(6)-a(7) from _Giovanni Resta_, Mar 28 2014

%E a(8)-a(15) from _Alois P. Heinz_, Jul 17 2014