A181955 Weighted sum of all cyclic subgroups of prime order in the Alternating group.

0, 0, 3, 18, 90, 390, 2205, 10878, 45318, 256350, 5530305, 55869330, 865551258, 9892489698, 78223384785, 470010394350, 24530527675230, 409760923017198, 10595007772540113, 160826214447439770, 1585844008081570650, 16787211082925012730, 1362379219330719093273

Offset

1,3

Comments

Sum of p for all p-subgroups in Alt_n.

Links

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

Formula

a(n) = A181954(n) - 2*A001465(n). - Andrew Howroyd, Jul 03 2018

Prog

(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/(p-1)))} \\ Andrew Howroyd, Jul 03 2018

Crossrefs

Cf. A181951 (number of such subgroups).

Cf. A181954 (symmetric case).

Cf. A001465.

Sequence in context: A290331 A124811 A006568 * A147518 A088336 A133594

Adjacent sequences: A181952 A181953 A181954 * A181956 A181957 A181958

Keyword

nonn

Author

Olivier Gérard, Apr 03 2012

Extensions

Terms a(9) and beyond from Andrew Howroyd, Jul 03 2018

Status

approved