a(n) = A000055(n) - 2.

Terms

a(0) =0a(1) =1a(2) =4a(3) =9a(4) =21a(5) =45a(6) =104a(7) =233a(8) =549a(9) =1299a(10) =3157a(11) =7739a(12) =19318a(13) =48627a(14) =123865a(15) =317953a(16) =823063a(17) =2144503a(18) =5623754a(19) =14828072a(20) =39299895a(21) =104636888a(22) =279793448a(23) =751065458a(24) =2023443030a(25) =5469566583a(26) =14830871800a(27) =40330829028a(28) =109972410219a(29) =300628862478