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A239759
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Number of pairs of functions (f,g) from a set of n elements into itself satisfying f(g(x)) = g(f(g(x))).
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1
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1, 1, 8, 147, 5032, 274765, 21702096, 2327543743, 324317092352, 56816985879801, 12201268360672000, 3147485927264980411, 959356469360927222784, 340785570064053310187173, 139449094593887763170361344, 65080820095941557895304404375
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MATHEMATICA
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Unprotect[Power]; 0^0 = 1;
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}]];
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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