A000136(n)/2.

Terms

a(0) =1a(1) =3a(2) =8a(3) =25a(4) =72a(5) =231a(6) =696a(7) =2268a(8) =7030a(9) =23155a(10) =73188a(11) =242957a(12) =778946a(13) =2601345a(14) =8430992a(15) =28289598a(16) =92470194a(17) =311472985a(18) =1025114180a(19) =3463982109a(20) =11465054942a(21) =38846071490a(22) =129180293184a(23) =438697998100