A298074 The number of k-cycles in the symmetric group on k symbols whose commutator with the standard k-cycle (1,2,...,k) is a k-cycle, where k = 2n-1.

1, 0, 10, 112, 7848, 525888

Offset

1,3

Comments

With the exception of the second term, it is not hard to prove that the sequence increases monotonically. Empirically, the growth is super-exponential.

For even k, there are no such k-cycles in S_k whose commutator with the standard k-cycle is a k-cycle.

Links

Table of n, a(n) for n=1..6.

Crossrefs

Sequence in context: A239651 A014484 A110040 * A181042 A263370 A129866

Adjacent sequences: A298071 A298072 A298073 * A298075 A298076 A298077

Keyword

nonn,more

Author

Tarik Aougab, Jan 11 2018

Status

approved