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

1,3

Comments

Row sums equal n! by definition.

Links

Table of n, a(n) for n=1..56.

R. Stanley, Hook Lengths and Contents, slide 28

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}]

Crossrefs

Cf. A191714.

Sequence in context: A138093 A138094 A060821 * A286777 A286123 A253243

Adjacent sequences: A191715 A191716 A191717 * A191719 A191720 A191721

Keyword

nonn,tabl

Author

Wouter Meeussen, Jun 12 2011

Status

approved