A239781 Number of pairs of functions f, g from a size n set into itself satisfying f(g(x)) = f(f(g(x))).
1, 1, 12, 321, 15280, 1127745, 118507536, 16731979033, 3044595017472, 692050790547297, 191796657547052800, 63563842088104098081, 24793529117087476242432, 11232023076988690608825505, 5843573099019743656060348416, 3457799186387568447755745563625
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..200
Programs
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Maple
a:= n-> add(binomial(n, k)*add(binomial(n-k, i)*k^i* (n-k-1)^(n-k-i)*(k+i)^n, i=0..n-k), k=0..n): seq(a(n), n=0..20); # Alois P. Heinz, Jul 17 2014 -
Mathematica
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 *)
Formula
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
Extensions
a(6)-a(7) from Giovanni Resta, Mar 28 2014
a(8)-a(15) from Alois P. Heinz, Jul 17 2014