OFFSET
1,1
COMMENTS
Let G, the group of rotations in n-dimensional Euclidean space, act on the set of (2^n)! paintings of an n-orthoplex bound by 2^n cells of dimension n-1. There are (2^n)! fixed points in the action table since the only element in G that leaves a painting fixed is the identity element. The order of G is 2^(n-1)*n! = A002866(n). So by Burnside's Lemma a(n) = (2^n)!/|G|.
LINKS
Frank M Jackson, Table of n, a(n) for n = 1..8
Wikipedia, Cross-polytope
FORMULA
a(n) = (2^n)!/(2^(n-1)*n!) = (2^n)!/A002866(n).
a(n) = 2 * A000723(n). - Alois P. Heinz, Aug 15 2018
MATHEMATICA
a[n_]:=(2^n)!/(2^(n-1)*n!); Array[a, 10]
CROSSREFS
KEYWORD
nonn
AUTHOR
Frank M Jackson, Aug 13 2018
STATUS
approved