a(n) = (1/4) * Sum_{k=0..n} (k+2) * 2^(n-k) * binomial(2*k+2,2*n-2*k+1).

Terms

a(0) =1a(1) =3a(2) =12a(3) =50a(4) =179a(5) =661a(6) =2390a(7) =8476a(8) =29909a(9) =104519a(10) =362672a(11) =1251478a(12) =4295783a(13) =14680713a(14) =49976442a(15) =169541536a(16) =573390953a(17) =1933856347a(18) =6505983668a(19) =21838288442a(20) =73152323803a(21) =244578237373a(22) =816308965214