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A290961
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Number of endofunctions on [n] such that the LCM of their cycle lengths equals n.
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3
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1, 1, 2, 6, 24, 840, 720, 5040, 40320, 59814720, 3628800, 83701537920, 479001600, 26980643289600, 2642646473026560, 1307674368000, 20922789888000, 41837259585747225600, 6402373705728000, 598354114828973074790400, 18160977780223038067507200
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OFFSET
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1,3
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LINKS
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FORMULA
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MAPLE
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b:= proc(n, m) option remember; `if`(n=0, x^m, add((j-1)!*
b(n-j, ilcm(m, j))*binomial(n-1, j-1), j=1..n))
end:
a:= n-> add(coeff(b(j, 1), x, n)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=1..25);
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MATHEMATICA
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b[n_, m_] := b[n, m] = If[n == 0, x^m, Sum[(j - 1)!*
b[n - j, LCM[m, j]]*Binomial[n - 1, j - 1], {j, 1, n}]];
a[n_] := Sum[Coefficient[b[j, 1], x, n]*n^(n-j)*Binomial[n-1, j-1], {j, 0, n}];
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CROSSREFS
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Cf. A074351 (the same for permutations).
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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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