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%I #27 Oct 04 2019 08:48:10
%S 1,1,8,147,5032,274765,21702096,2327543743,324317092352,
%T 56816985879801,12201268360672000,3147485927264980411,
%U 959356469360927222784,340785570064053310187173,139449094593887763170361344,65080820095941557895304404375
%N Number of pairs of functions (f,g) from a set of n elements into itself satisfying f(g(x)) = g(f(g(x))).
%H Alois P. Heinz, <a href="/A239759/b239759.txt">Table of n, a(n) for n = 0..241</a>
%F a(n) = Sum_{k=0..n} C(n,k) * k^k * (Sum_{j=0..n-k} C(n-k,j)*k^j*(j+k-1)^j*((n-k)*(j+k))^(n-j-k)). - _David Einstein_, Oct 11 2016
%t Unprotect[Power]; 0^0 = 1;
%t a[n_] := If[n == 0, 1, Sum[Binomial[n, k] k^k Sum[Binomial[n - k, j] k^j (j + k - 1)^j ((n - k)(j + k))^(n - j - k), {j, 0, n - k}], {k, 1, n}]];
%t a /@ Range[0, 15] (* _Jean-François Alcover_, Oct 04 2019 *)
%o (PARI) a(n) = if(n==0,1,sum(k=1,n, binomial(n,k) * k^k * (sum(j=0,n-k, binomial(n-k,j)*k^j*(j+k-1)^j*((n-k)*(j+k))^(n-j-k))))) \\ _Joerg Arndt_, Oct 13 2016
%Y Cf. A000248, A000949.
%K nonn
%O 0,3
%A _Chad Brewbaker_, Mar 26 2014
%E a(6)-a(7) from _Giovanni Resta_, Mar 28 2014
%E a(8)-a(15) from _David Einstein_, Oct 11 2016
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