G.f. satisfies A(x) = 1 + x*cycle_index(Sym(5), A(x)).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =9a(6) =20a(7) =47a(8) =112a(9) =277a(10) =693a(11) =1766a(12) =4547a(13) =11852a(14) =31146a(15) =82534a(16) =220149a(17) =590834a(18) =1593951a(19) =4320723a(20) =11761394a(21) =32138301a(22) =88121176a(23) =242383729a(24) =668607115a(25) =1849194691a(26) =5126800907a(27) =14245679652a(28) =39666239726a(29) =110661514973