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%I #8 Jul 16 2014 19:21:35
%S 1,1,12,189,5200,208945,11517936,828676933
%N Number of pairs of functions f, g from a size n set into itself satisfying f(f(g(x))) = g(g(f(x))).
%p s:= proc(n, i) option remember; `if`(i=0, [[]],
%p map(x-> seq([j, x[]], j=1..n), s(n, i-1)))
%p end:
%p a:= proc(n) (l-> add(add(`if`([true$n]=[seq(evalb(
%p f[f[g[i]]]=g[g[f[i]]]), i=1..n)], 1, 0), g=l), f=l))(s(n$2))
%p end:
%p seq(a(n), n=0..5); # _Alois P. Heinz_, Jul 16 2014
%Y Cf. A181162, A239769, A239773.
%K nonn,more
%O 0,3
%A _Chad Brewbaker_, Mar 26 2014
%E a(6)-a(7) from _Giovanni Resta_, Mar 28 2014
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