Fourth column (k=3) of triangle A084938.

Terms

a(0) =1a(1) =3a(2) =9a(3) =31a(4) =126a(5) =606a(6) =3428a(7) =22572a(8) =170856a(9) =1467432a(10) =14123808a(11) =150644448a(12) =1763377344a(13) =22466496960a(14) =309371685120