a(n) = Sum_{j=1..floor(n/2)} binomial(n+j-1,j-1).

Terms

a(0) =0a(1) =1a(2) =1a(3) =6a(4) =7a(5) =36a(6) =45a(7) =220a(8) =286a(9) =1365a(10) =1820a(11) =8568a(12) =11628a(13) =54264a(14) =74613a(15) =346104a(16) =480700a(17) =2220075a(18) =3108105a(19) =14307150a(20) =20160075a(21) =92561040a(22) =131128140a(23) =600805296a(24) =854992152a(25) =3910797436a(26) =5586853480a(27) =25518731280a(28) =36576848168a(29) =166871334960