A074103 - OEIS

%I #16 May 24 2019 17:16:00

%S 1,1,2,3,4,6,3,12,15,20,30,15,60,60,84,105,140,210,105,420,420,420,

%T 315,840,840,1260,1260,1540,2310,2520,4620,4620,5460,5460,9240,9240,

%U 13860,13860,16380,16380,27720,30030,32760,60060,60060,60060,45045,120120

%N a(n) = n!/A074859(n).

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

%H Alois P. Heinz, <a href="/A074103/b074103.txt">Table of n, a(n) for n = 0..175</a>

%t g[n_] := g[n] = Max[LCM @@@ IntegerPartitions[n]];

%t f[x_, n_] := Total[(MoebiusMu[g[n]/#]*Exp[Total[(x^#/#&) /@ Divisors[#]]]&) /@ Divisors[g[n]]];

%t a[0] = 1; a[n_] := 1/SeriesCoefficient[f[x, n], {x, 0, n}];

%t Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, May 24 2019 *)

%Y Cf. A074859, A000793.

%K nonn

%O 0,3

%A _Vladeta Jovovic_, Sep 15 2002

%E More terms from _Max Alekseyev_, Jun 13 2011