A206820 a(n) is the sum of the squares of the sizes of the conjugacy classes in the symmetric group A_n.

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.

Links

Table of n, a(n) for n=1..18.

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

Adjacent sequences: A206817 A206818 A206819 * A206821 A206822 A206823

Keyword

nonn,nice,easy

Author

Olivier Gérard, Feb 12 2012

Extensions

More terms from Eric M. Schmidt, Jan 26 2014

Status

approved