A360808 Number of double cosets of the Sylow 2-subgroup of the symmetric group S_n.

1, 2, 2, 2, 8, 8, 35, 16, 51, 145, 1112, 1145, 10929, 41400, 542785, 40384, 583169, 2781808, 48558706, 65461347, 1277941540, 7370563251, 159694747220, 63387056365, 1500631724572, 10152855622657

Offset

1,2

Comments

Let Syl_2(n) denote the Sylow 2-subgroup of the symmetric group S_n. Then a(n) is the number of double cosets Syl_2(n)wSyl_2(n).

Links

Table of n, a(n) for n=1..26.

Formula

Define a symmetric function T_k recursively by T_0 = p_1 (power sum), and T_k is the plethysm h_2[T_{k-1}] for k>0. If n has the binary expansion 2^{a_0} + 2^{a_1} + ..., then set $U_n = T_{a_0}T_{a_1}... Then a_n = <U_n,U_n> (usual scalar product on symmetric functions).

Crossrefs

Sequence in context: A275928 A221072 A339162 * A168272 A222448 A360309

Adjacent sequences: A360805 A360806 A360807 * A360809 A360810 A360811

Keyword

nonn

Author

Richard Stanley, Feb 21 2023

Status

approved