A181951 Number of cyclic subgroups of prime order in the Alternating Group A_n.

0, 0, 1, 7, 31, 121, 526, 2227, 9283, 54931, 694156, 6104011, 76333687, 872550043, 7491293356, 49469173951, 1571562887071, 24729107440927, 584036983443568, 8662243014551731, 87570785839885951, 1147293350653737211, 66175018194591458692, 1378758190497550145383

Offset: 1

Author

Olivier Gérard, Apr 03 2012

Keywords

• nonn

Links

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

Crossrefs

Cf. A001465, A181955, A186202 (symmetric group).

Programs

Mathematica

a[n_] := Sum[If[PrimeQ[p], Sum[If[p > 2 || Mod[k, 2] == 0, n!/(k!*(n - k*p)!*p^k)/(p - 1), 0], {k, 1, n/p}], 0], {p, 2, n}];
Array[a, 24] (* Jean-François Alcover, Jul 06 2018, after Andrew Howroyd *)

PARI

a(n)={sum(p=2, n, if(isprime(p), sum(k=1, n\p, if(p>2||k%2==0, n!/(k!*(n-k*p)!*p^k)))/(p-1)))}

Formula

a(n) = A186202(n) - A001465(n). - Andrew Howroyd, Jul 04 2018

Extensions

Terms a(9) and beyond from Andrew Howroyd, Jul 04 2018