Number of Dyck paths with n nodes and altitude 3.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =6a(5) =21a(6) =68a(7) =208a(8) =612a(9) =1752a(10) =4916a(11) =13588a(12) =37128a(13) =100548a(14) =270404a(15) =723208a(16) =1925844a(17) =5110644a(18) =13524872a(19) =35713828a(20) =94140900a(21) =247806600a(22) =651572660a(23) =1711695508a(24) =4493475336a(25) =11789439876a(26) =30917835908a(27) =81053196808a(28) =212426303892a(29) =556607396532