Certain directed lattice paths.

Terms

a(0) =1a(1) =6a(2) =35a(3) =207a(4) =1251a(5) =7678a(6) =47658a(7) =298371a(8) =1880659a(9) =11918586a(10) =75871710a(11) =484793950a(12) =3107494430a(13) =19973075580a(14) =128678167220a(15) =830735862179