a(n) = A000055(n) - 1.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =1a(5) =2a(6) =5a(7) =10a(8) =22a(9) =46a(10) =105a(11) =234a(12) =550a(13) =1300a(14) =3158a(15) =7740a(16) =19319a(17) =48628a(18) =123866a(19) =317954a(20) =823064a(21) =2144504a(22) =5623755a(23) =14828073a(24) =39299896a(25) =104636889a(26) =279793449a(27) =751065459a(28) =2023443031a(29) =5469566584