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A239771
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Number of pairs of functions (f,g) from a size n set into itself satisfying f(x) = g(g(f(x))).
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4
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1, 1, 10, 213, 8056, 465945, 37823616, 4075467781, 560230714240, 95369455852497, 19643693349548800, 4805295720474420501, 1374890520609054683136, 454286686896040037996905, 171479277693049020232695808, 73262491601904459123264721125, 35143072854722729593790081499136
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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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MAPLE
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g:= proc(n) g(n):= `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
a:= n-> add(binomial(n, k)*Stirling2(n, k)*k!*
add(binomial(n-k, i)*binomial(k, i)*i!*
g(k-i)*n^(n-k-i), i=0..min(k, n-k)), k=0..n):
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MATHEMATICA
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g[n_] := g[n] = If[n < 2, 1, g[n-1] + (n-1)*g[n-2]];
a[n_] := If[n == 0, 1, Sum[Binomial[n, k]*StirlingS2[n, k]*k!*Sum[ Binomial[n-k, i]*Binomial[k, i]*i!*g[k-i]*n^(n-k-i), {i, 0, Min[k, n-k]} ], {k, 0, n}]];
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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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