A096611 a(n)=number of Catalan knight paths in right half-plane from (0,0) to (n,2).

0, 1, 0, 3, 1, 16, 18, 95, 154, 581, 1160, 3752, 8485, 25208, 61180, 173343, 438242, 1210222, 3134472, 8538629, 22437042, 60690510, 160889234, 433701996, 1156122902, 3112018729, 8325803356, 22402792752, 60084101129, 161701735578