a(n) = binomial(2*n + 2, n + 2) - 1.

Terms

a(0) =0a(1) =3a(2) =14a(3) =55a(4) =209a(5) =791a(6) =3002a(7) =11439a(8) =43757a(9) =167959a(10) =646645a(11) =2496143a(12) =9657699a(13) =37442159a(14) =145422674a(15) =565722719a(16) =2203961429a(17) =8597496599a(18) =33578000609a(19) =131282408399a(20) =513791607419