a(n) = Sum_{k=0..n} 3^k*A111146(n,k).

Terms

a(0) =1a(1) =3a(2) =18a(3) =117a(4) =801a(5) =5724a(6) =42633a(7) =331911a(8) =2717874a(9) =23620329a(10) =220260789a(11) =2228505372a(12) =24681015981a(13) =300506801715