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%I #5 Feb 21 2023 17:31:45
%S 1,2,2,2,8,8,35,16,51,145,1112,1145,10929,41400,542785,40384,583169,
%T 2781808,48558706,65461347,1277941540,7370563251,159694747220,
%U 63387056365,1500631724572,10152855622657
%N Number of double cosets of the Sylow 2-subgroup of the symmetric group S_n.
%C 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).
%F 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).
%K nonn
%O 1,2
%A _Richard Stanley_, Feb 21 2023