A036725 G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 2 generated by (1,2)(3,4)(5,6)(7,8).
1, 1, 4, 32, 268, 2574, 26004, 274752, 2990412, 33321801, 378155340, 4355839608, 50792907100, 598432565856, 7112882558060, 85186232560504, 1026982086302284, 12453151958594288, 151785836438975264, 1858565360218893144, 22851521570687098564
Offset: 0