login
A206820
a(n) is the sum of the squares of the sizes of the conjugacy classes in the symmetric group A_n.
3
1, 1, 3, 42, 914, 23694, 1048542, 45379878, 3272115926, 257662344206, 27726935045366, 3101635433302996, 474878584235678020, 76786899439922296204, 15844064187141655171020, 3326909755872288926885670, 897661138669999282018222470, 246381314116108359863665821750
OFFSET
1,3
COMMENTS
a(n) is the sum over all elements of Alt_n of the size of their conjugacy class. Each conjugacy class is thus counted as many times as its size, giving a sum of squares.
EXAMPLE
For n=5, a(5) = 1 + 12^2 + 12^2 + 15^2 + 20^2 = 914.
The class equation of A_5 is 1 + 12 + 12 + 15 + 20 = 60 = 5!/2
PROG
(GAP) A206820 := n -> Sum(ConjugacyClasses(AlternatingGroup(n)), c->Size(c)^2); # Eric M. Schmidt, Jan 26 2014
CROSSREFS
A087132 (sequence for S_n), A000702 (conjugacy classes in A_n)
Sequence in context: A336572 A366006 A366010 * A157542 A078601 A268621
KEYWORD
nonn,nice,easy
AUTHOR
Olivier Gérard, Feb 12 2012
EXTENSIONS
More terms from Eric M. Schmidt, Jan 26 2014
STATUS
approved