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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified January 16 15:31 EST 2019. Contains 319195 sequences. (Running on oeis4.)