A variant of the recurrence for A001190.

Terms

a(0) =0a(1) =1a(2) =1a(3) =1a(4) =2a(5) =2a(6) =5a(7) =7a(8) =17a(9) =29a(10) =66a(11) =126a(12) =284a(13) =568a(14) =1281a(15) =2662a(16) =6017a(17) =12756a(18) =28992a(19) =62621a(20) =142801a(21) =312129a(22) =714760a(23) =1578706a(24) =3626762a(25) =8074580a(26) =18606900a(27) =41716797a(28) =96374235a(29) =217271226