OFFSET
0,3
COMMENTS
Also pairs of functions where f(f(f(x))) = g(f(f(x))).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..160
FORMULA
a(n) = n! Sum_{d = 0..n} n^(n-d) Sum_{c = 0..(n-d)/2} S2(c+d,d) Sum_{b = c..n-c-d} S2(b,c)/(b! (n-b-c-d)!) d^(n-b-c-d). - David Einstein, Oct 23 2016
MATHEMATICA
t1[n_, d_, c_] := StirlingS2[c + d, d] Sum[ StirlingS2[b, c]/(b! (n - b - c - d)!) d^(n - b - c - d), {b, c, n - c - d}]
a[n_] := If[n == 0, 1, n! Sum[n^(n - d) Sum[t1[n, d, c], {c, 0, Floor[(n - d)/2]}], {d, 1, n}]]
Table[a[n], {n, 0, 20}] (* David Einstein, Oct 23 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Chad Brewbaker, Mar 26 2014
EXTENSIONS
a(6)-a(7) from Giovanni Resta, Mar 28 2014
a(8)-a(10) from Paul Boddington, Feb 23 2015
a(11)-a(16) from David Einstein, Oct 23 2016
STATUS
approved