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A239781
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Number of pairs of functions f, g from a size n set into itself satisfying f(g(x)) = f(f(g(x))).
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1
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1, 1, 12, 321, 15280, 1127745, 118507536, 16731979033, 3044595017472, 692050790547297, 191796657547052800, 63563842088104098081, 24793529117087476242432, 11232023076988690608825505, 5843573099019743656060348416, 3457799186387568447755745563625
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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) * Sum_{i=0..n-k} C(n-k,i) * k^i * (n-k-1)^(n-k-i) * (k+i)^n. - Alois P. Heinz, Jul 17 2014
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MAPLE
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a:= n-> add(binomial(n, k)*add(binomial(n-k, i)*k^i*
(n-k-1)^(n-k-i)*(k+i)^n, i=0..n-k), k=0..n):
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MATHEMATICA
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Unprotect[Power]; 0^0 = 1; a[n_] := Sum[Binomial[n, k]*Sum[Binomial[n-k, i]*k^i*(n-k-1)^(n-k-i)*(k+i)^n, {i, 0, n-k}], {k, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 28 2017, after Alois P. Heinz *)
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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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