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A036726
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G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = cyclic group of order 3 generated by (1,2,3)(4,5,6).
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12
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1, 1, 2, 9, 46, 247, 1436, 8684, 54102, 345042, 2241014, 14771896, 98568908, 664518873, 4519394316, 30969650840, 213625862342, 1482134240438, 10335968352644, 72411026552273, 509383556655134, 3596650497366507, 25480925906761956
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