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

1,4

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

Formula

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

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 *)

Crossrefs

Cf. A002826.

Sequence in context: A309774 A244296 A143046 * A228279 A009197 A205336

Adjacent sequences: A246066 A246067 A246068 * A246070 A246071 A246072

Keyword

nonn

Author

Sean A. Irvine, Aug 25 2014

Status

approved