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A348590
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Number of endofunctions on [n] with exactly one isolated fixed point.
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2
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0, 1, 0, 9, 68, 845, 12474, 218827, 4435864, 102030777, 2625176150, 74701061831, 2329237613988, 78972674630005, 2892636060014050, 113828236497224355, 4789121681108775344, 214528601554419809777, 10193616586275094959534, 512100888749268955942015
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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a(3) = 9: 122, 133, 132, 121, 323, 321, 113, 223, 213.
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MAPLE
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g:= proc(n) option remember; add(n^(n-j)*(n-1)!/(n-j)!, j=1..n) end:
b:= proc(n, t) option remember; `if`(n=0, t, add(g(i)*
b(n-i, `if`(i=1, 1, t))*binomial(n-1, i-1), i=1+t..n))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..23);
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MATHEMATICA
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g[n_] := g[n] = Sum[n^(n - j)*(n - 1)!/(n - j)!, {j, 1, n}] ;
b[n_, t_] := b[n, t] = If[n == 0, t, Sum[g[i]*
b[n - i, If[i == 1, 1, t]]*Binomial[n - 1, i - 1], {i, 1 + t, n}]];
a[n_] := b[n, 0];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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