Triangle T(n,t) by rows: The number of rooted forests with n 3-colored nodes and t rooted trees.

Terms

a(0) =3a(1) =9a(2) =6a(3) =45a(4) =27a(5) =10a(6) =246a(7) =180a(8) =54a(9) =15a(10) =1485a(11) =1143a(12) =405a(13) =90a(14) =21a(15) =9432a(16) =7704a(17) =2856a(18) =720a(19) =135a(20) =28a(21) =62625a(22) =52731a(23) =20682a(24) =5385a(25) =1125a(26) =189a(27) =36a(28) =428319a(29) =369969