login
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

%I #7 Mar 30 2012 18:37:45

%S 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,

%T 1540,0,232,0,13488,0,18956,0,7112,0,764,40320,0,161936,0,125580,0,

%U 32424,0,2620,0,1011456,0,1648160,0,808248,0,151440,0,9496,3628800

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

%C Row sums equal n! by definition.

%H R. Stanley, <a href="http://www-math.mit.edu/~rstan/transparencies/hooks.pdf">Hook Lengths and Contents, slide 28</a>

%t (* slow *)

%t Table[Rest@ CoefficientList[ Apply[Plus, (q^Length[ToCycles[# [[#]] ]])& /@ Permutations[n] ] ,q],{n,6}]

%t (* fast, content[] see A191714 *)

%t Table[Rest@ CoefficientList[ Apply[Plus, NumberOfTableaux[#]Apply[Times,q+Flatten[content[#]]]& /@ Partitions[n]] ,q],{n,6}]

%Y Cf. A191714.

%K nonn,tabl

%O 1,3

%A _Wouter Meeussen_, Jun 12 2011