From enumerating paths in the plane.

Terms

a(0) =0a(1) =1a(2) =42a(3) =594a(4) =4719a(5) =26026a(6) =111384a(7) =395352a(8) =1215126a(9) =3331251a(10) =8321170a(11) =19240650a(12) =41683005a(13) =85408596a(14) =166768096a(15) =312203232a(16) =563178924a(17) =982981701a(18) =1665911754a(19) =2749500754a(20) =4430505387a(21) =6985558206a(22) =10797503640a(23) =16388608600a(24) =24462014850a(25) =35952994935a(26) =52091785746