a(n)=number of Catalan knight paths in right half-plane from (0,0) to (n,n).

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =4a(5) =4a(6) =6a(7) =30a(8) =58a(9) =76a(10) =196a(11) =528a(12) =1010a(13) =1860a(14) =4470a(15) =10416a(16) =20762a(17) =43272a(18) =99568a(19) =219198a(20) =457862a(21) =993192a(22) =2221840a(23) =4833382a(24) =10372864a(25) =22752468a(26) =50238288a(27) =109413330a(28) =238079388a(29) =523375136