a(n) = Sum_{i=0..floor(n/2)} T(i,n-i), array T as in A047072.

Terms

a(0) =1a(1) =1a(2) =3a(3) =2a(4) =5a(5) =6a(6) =14a(7) =20a(8) =45a(9) =70a(10) =154a(11) =252a(12) =546a(13) =924a(14) =1980a(15) =3432a(16) =7293a(17) =12870a(18) =27170a(19) =48620a(20) =102102a(21) =184756a(22) =386308a(23) =705432a(24) =1469650a(25) =2704156a(26) =5616324a(27) =10400600a(28) =21544100a(29) =40116600