A060015 Sum of orders of all even permutations of n letters.

1, 1, 7, 31, 211, 1411, 12601, 137047, 1516831, 18111751, 223179001, 2973194071, 46287964867, 835826439631, 15722804528341, 292673102609791, 5177400032329231, 102538737981192607, 2284570602107946601

Offset: 1

Author

N. J. A. Sloane, Mar 17 2001

Keywords

• nonn
• nice
• easy

Examples

			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.
		

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.

Crossrefs

Cf. A060014.

Programs

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 *)

Extensions

More terms from Vladeta Jovovic, Mar 18 2001