G.f.: A(x) = x*cycle_index(S5, B(x)-1), where B(x) is g.f. for A000598.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =1a(7) =1a(8) =3a(9) =7a(10) =18a(11) =43a(12) =111a(13) =276a(14) =711a(15) =1819a(16) =4713a(17) =12221a(18) =31929a(19) =83594a(20) =219877a(21) =579868a(22) =1534177a(23) =4068918a(24) =10818821a(25) =28827430a(26) =76972091a(27) =205904447a(28) =551774917a(29) =1481015145