OFFSET
0,3
COMMENTS
As observed by Yuval Filmus, this also counts pairs (f,g) that satisfy g(f(x)) = f^{k}(x) for k >= 1. - Chad Brewbaker, Mar 27 2014
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
Yuval Filmus, Answer to 'A curious Wilf equivalence class of function compositions', Mar 27 2014
FORMULA
a(n) = Sum_{k=0..n} C(n,k) * k^n * (n-1)^(n-k) = Sum_{k=0..n} C(n,k) * A048993(n,k) * k! * n^(n-k). - Alois P. Heinz, Jul 23 2014
MAPLE
a:= n-> add(binomial(n, k)*k^n*(n-1)^(n-k), k=0..n):
seq(a(n), n=0..20); # Alois P. Heinz, Jul 23 2014
MATHEMATICA
a[n_] := If[n<2, 1, Sum[Binomial[n, k]*k^n*(n-1)^(n-k), {k, 0, n}]];
a /@ Range[0, 20] (* Jean-François Alcover, Oct 03 2019, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Chad Brewbaker, Mar 26 2014
EXTENSIONS
a(6)-a(7) from Giovanni Resta, Mar 26 2014
a(8)-a(16) from Alois P. Heinz, Jul 17 2014
STATUS
approved