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

1,4

Links

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

Formula

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

Prog

(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

Crossrefs

Cf. A051625, A074260.

Sequence in context: A082980 A157536 A046488 * A225884 A115647 A019437

Adjacent sequences: A074877 A074878 A074879 * A074881 A074882 A074883

Keyword

nonn

Author

Vladeta Jovovic, Sep 30 2002

Extensions

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

Status

approved