A191718 - OEIS

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

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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 *)