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

1,2

Links

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

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

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 *)

Crossrefs

Cf. A088994, A060632.

Cf. A000085, A001189.

Sequence in context: A154919 A019230 A298148 * A013140 A326773 A241211

Adjacent sequences: A088039 A088040 A088041 * A088043 A088044 A088045

Keyword

nonn

Author

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

Extensions

More terms from Vladeta Jovovic, Nov 03 2003

Status

approved