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

Terms

a(0) =1a(1) =2a(2) =7a(3) =40a(4) =137a(5) =526a(6) =1979a(7) =7092a(8) =25485a(9) =90266a(10) =316415a(11) =1102336a(12) =3813841a(13) =13123366a(14) =44947139a(15) =153295692a(16) =520920213a(17) =1764401586a(18) =5958744327a(19) =20071157144a(20) =67446281689a(21) =226154549822a(22) =756826028235