A074103 a(n) = n!/A074859(n).

1, 1, 2, 3, 4, 6, 3, 12, 15, 20, 30, 15, 60, 60, 84, 105, 140, 210, 105, 420, 420, 420, 315, 840, 840, 1260, 1260, 1540, 2310, 2520, 4620, 4620, 5460, 5460, 9240, 9240, 13860, 13860, 16380, 16380, 27720, 30030, 32760, 60060, 60060, 60060, 45045, 120120

Offset: 0

Author

Vladeta Jovovic, Sep 15 2002

Keywords

• nonn

Comments

1/a(n) is probability that a random degree-n permutation has the maximum possible order.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..175

Crossrefs

Cf. A074859, A000793.

Programs

Mathematica

g[n_] := g[n] = Max[LCM @@@ IntegerPartitions[n]];
f[x_, n_] := Total[(MoebiusMu[g[n]/#]*Exp[Total[(x^#/#&) /@ Divisors[#]]]&) /@ Divisors[g[n]]];
a[0] = 1; a[n_] := 1/SeriesCoefficient[f[x, n], {x, 0, n}];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, May 24 2019 *)

Extensions

More terms from Max Alekseyev, Jun 13 2011