G.f. satisfies A(x) = 1 + x*cycle_index(Sym(6), A(x)).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =9a(6) =20a(7) =48a(8) =114a(9) =283a(10) =710a(11) =1816a(12) =4690a(13) =12267a(14) =32338a(15) =85978a(16) =230080a(17) =619521a(18) =1676808a(19) =4560286a(20) =12454272a(21) =34143682a(22) =93928091a(23) =259208006a(24) =717375068a(25) =1990625390a(26) =5537142610a(27) =15436744525a(28) =43124847431a(29) =120708508008