A088042 Number of permutations in the symmetric group S_n such that the size of their conjugacy class is odd.

1, 2, 4, 4, 16, 76, 232, 106, 946, 5716, 27776, 63856, 272416, 2390480, 10349536, 2027026, 34459426, 344594404, 2618916472, 10475679736, 54997260256, 568305978472, 3132225435824, 1807129471456, 12047128545376, 175289251587776, 1326384554695552

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 02 2003

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A088994, A060632.

Cf. A000085, A001189.

Programs

Maple

a:= n-> n!*add((binomial(n-(n mod 2), 2*k) mod 2)/((n-2*k)!*k!*2^k),
        k=0..floor(n/2)):
seq(a(n), n=1..30);  # Alois P. Heinz, May 01 2013

Mathematica

a[n_] := n!*Sum[Mod[Binomial[n-Mod[n, 2], 2*k], 2]/((n-2*k)!*k!*2^k), {k, 0, Floor[n/2]}]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 17 2014, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=0..floor(n/2)} n!/(n-2*k)!/k!/2^k*(C(n-(n mod 2), 2*k) mod 2). - Vladeta Jovovic, Nov 06 2003

Extensions

More terms from Vladeta Jovovic, Nov 03 2003