A191718 a(n,k) is the count of permutations with cycle length k in the products w*w over all permutations w of length n.

1, 0, 2, 2, 0, 4, 0, 14, 0, 10, 24, 0, 70, 0, 26, 0, 304, 0, 340, 0, 76, 720, 0, 2548, 0, 1540, 0, 232, 0, 13488, 0, 18956, 0, 7112, 0, 764, 40320, 0, 161936, 0, 125580, 0, 32424, 0, 2620, 0, 1011456, 0, 1648160, 0, 808248, 0, 151440, 0, 9496, 3628800

Offset: 1

Author

Wouter Meeussen, Jun 12 2011

Keywords

• nonn
• tabl

Comments

Row sums equal n! by definition.

Links

• R. Stanley, Hook Lengths and Contents, slide 28

Crossrefs

Cf. A191714.

Programs

Mathematica

(* slow *)
Table[Rest@ CoefficientList[ Apply[Plus, (q^Length[ToCycles[# [[#]] ]])&  /@ Permutations[n] ] ,q],{n,6}]
(* fast, content[] see A191714 *)
Table[Rest@ CoefficientList[ Apply[Plus, NumberOfTableaux[#]Apply[Times,q+Flatten[content[#]]]& /@ Partitions[n]] ,q],{n,6}]