a(n) = (1/2!)*3^n*(n+3)*(n).

Terms

a(0) =6a(1) =45a(2) =243a(3) =1134a(4) =4860a(5) =19683a(6) =76545a(7) =288684a(8) =1062882a(9) =3838185a(10) =13640319a(11) =47829690a(12) =165809592a(13) =569173311a(14) =1937102445a(15) =6543101592a(16) =21953827710a(17) =73222472421a(18) =242912646603a(19) =801960412230