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A036724
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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).
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1
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1, 1, 3, 18, 109, 768, 5652, 43618, 346353, 2816526, 23321925, 196005552, 1667527836, 14333190427, 124283998707, 1085847441828, 9549523972105, 84471264138366, 751042470499425, 6708237169875867, 60164133936171522
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