A246069 Number of maximal classes determined by permutations.

0, 1, 1, 3, 6, 35, 120, 105, 1120, 19089, 362880, 133595, 39916800, 148397535, 458313856, 2027025, 1307674368000, 6133352225, 355687428096000, 40549021532019, 4139906028544000, 464463124401214575, 51090942171709440000, 1173011341727225

Offset: 1

Author

Sean A. Irvine, Aug 25 2014

Keywords

• nonn

Comments

Corresponds to r_2(k) in the Rosenberg paper.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..450
• Ivo Rosenberg, The number of maximal closed classes in the set of functions over a finite domain, J. Combinatorial Theory Ser. A 14 (1973), 1-7.
• Ivo Rosenberg and N. J. A. Sloane, Correspondence, 1971

Crossrefs

Cf. A002826.

Programs

Maple

a:= n -> add(n!/((n/p)! * p^(n/p) * (p-1)), p = numtheory:-factorset(n)):
seq(a(n), n=1..100); # Robert Israel, Aug 27 2014

Mathematica

a[n_] := If[n == 1, 0, Sum[n!/((n/p)! p^(n/p) (p-1)), {p, FactorInteger[n][[All, 1]]}]]; Array[a, 100] (* Jean-François Alcover, Mar 22 2019, after Robert Israel *)

Formula

a(n) = sum(n! / (m! * p^m * (p-1)), n = p * m, p prime). (corrected by Robert Israel, Aug 27 2014)