A074880 Number of labeled cyclic subgroups of S_n having order n.

1, 1, 1, 3, 6, 120, 120, 1260, 6720, 128520, 362880, 20041560, 39916800, 1132971840, 11721790080, 163459296000, 1307674368000, 87307501881600, 355687428096000, 19137704006453760, 205947392645030400, 5118231678995635200, 51090942171709440000, 4769913628444053196800

Offset: 1

Author

Vladeta Jovovic, Sep 30 2002

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A051625, A074260.

Programs

PARI

a(n)={n!*polcoeff(sumdiv(n, i, moebius(n/i)*exp(sumdiv(i, j, x^j/j) + O(x*x^n))), n)/eulerphi(n)} \\ Andrew Howroyd, Jul 02 2018

Formula

a(n) = A074351(n)/A000010(n).

Extensions

Terms a(22) and beyond from Andrew Howroyd, Jul 02 2018