login
A060015
Sum of orders of all even permutations of n letters.
5
1, 1, 7, 31, 211, 1411, 12601, 137047, 1516831, 18111751, 223179001, 2973194071, 46287964867, 835826439631, 15722804528341, 292673102609791, 5177400032329231, 102538737981192607, 2284570602107946601
OFFSET
1,3
LINKS
Joshua Harrington, Lenny Jones, and Alicia Lamarche, Characterizing Finite Groups Using the Sum of the Orders of the Elements, International Journal of Combinatorics, Volume 2014, Article ID 835125, 8 pages.
EXAMPLE
For n = 4 there is 1 even permutation (1) of order 1, 3 even permutations (12)(34) etc. of order 2 and 8 (123) etc. of order 3, for a total of 31.
MATHEMATICA
g[list_]:=Total[list]!/Apply[Times, list]/Apply[Times, Table[Count[list, n]!, {n, 1, 20}]]; f[list_]:=Apply[Plus, Table[Count[list, n], {n, 2, 20, 2}]]; Map[Total, Table[Map[g, Select[Partitions[n], EvenQ[f[#]]&]]*Map[Apply[LCM, #]&, Select[Partitions[n], EvenQ[f[#]]&]], {n, 1, 20}]] (* Geoffrey Critzer, Mar 26 2013 *)
CROSSREFS
Cf. A060014.
Sequence in context: A155521 A201116 A329944 * A261558 A241456 A094711
KEYWORD
nonn,nice,easy
AUTHOR
N. J. A. Sloane, Mar 17 2001
EXTENSIONS
More terms from Vladeta Jovovic, Mar 18 2001
STATUS
approved