Number of balanced parenthesis expressions of length 2n and depth 3.

Terms

a(0) =1a(1) =5a(2) =18a(3) =57a(4) =169a(5) =482a(6) =1341a(7) =3669a(8) =9922a(9) =26609a(10) =70929a(11) =188226a(12) =497845a(13) =1313501a(14) =3459042a(15) =9096393a(16) =23895673a(17) =62721698a(18) =164531565a(19) =431397285a(20) =1130708866a(21) =2962826465a(22) =7761964833a(23) =20331456642a(24) =53249182309a(25) =139449644717a(26) =365166860706a(27) =956185155129