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A290961
Number of endofunctions on [n] such that the LCM of their cycle lengths equals n.
3
1, 1, 2, 6, 24, 840, 720, 5040, 40320, 59814720, 3628800, 83701537920, 479001600, 26980643289600, 2642646473026560, 1307674368000, 20922789888000, 41837259585747225600, 6402373705728000, 598354114828973074790400, 18160977780223038067507200
OFFSET
1,3
LINKS
FORMULA
a(n) = A222029(n,n).
MAPLE
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);
MATHEMATICA
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}];
Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Mar 07 2022, after Alois P. Heinz *)
CROSSREFS
Main diagonal of A222029.
Cf. A074351 (the same for permutations).
Sequence in context: A110729 A088258 A227886 * A089718 A123150 A086591
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 15 2017
STATUS
approved