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

Terms

a(0) =0a(1) =2a(2) =3a(3) =2a(4) =5a(5) =7a(6) =14a(7) =26a(8) =51a(9) =103a(10) =209a(11) =435a(12) =910a(13) =1930a(14) =4122a(15) =8874a(16) =19227a(17) =41893a(18) =91751a(19) =201839a(20) =445841a(21) =988403a(22) =2198547a(23) =4905147a(24) =10974210a(25) =24615134a(26) =55341636a(27) =124694354a(28) =281525678a(29) =636802626