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A239776
Number of pairs of functions f, g from a size n set into itself satisfying f(f(g(x))) = g(g(f(x))).
0
1, 1, 12, 189, 5200, 208945, 11517936, 828676933
OFFSET
0,3
MAPLE
s:= proc(n, i) option remember; `if`(i=0, [[]],
map(x-> seq([j, x[]], j=1..n), s(n, i-1)))
end:
a:= proc(n) (l-> add(add(`if`([true$n]=[seq(evalb(
f[f[g[i]]]=g[g[f[i]]]), i=1..n)], 1, 0), g=l), f=l))(s(n$2))
end:
seq(a(n), n=0..5); # Alois P. Heinz, Jul 16 2014
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Chad Brewbaker, Mar 26 2014
EXTENSIONS
a(6)-a(7) from Giovanni Resta, Mar 28 2014
STATUS
approved