One fourth of third column (m=2) of triangle A142963.

Terms

a(0) =1a(1) =18a(2) =129a(3) =646a(4) =2685a(5) =10002a(6) =34777a(7) =115566a(8) =372453a(9) =1175290a(10) =3654369a(11) =11245110a(12) =34349005a(13) =104373282a(14) =315969705a(15) =954002878a(16) =2874983541a(17) =8652474378a(18) =26015617585a(19) =78169534470a(20) =234766551261a(21) =704840716978