Sum(C(j)*(n-j)*4^(n-j),j=0..n-1), C = Catalan numbers.

Terms

a(0) =0a(1) =4a(2) =36a(3) =232a(4) =1300a(5) =6744a(6) =33320a(7) =159184a(8) =742068a(9) =3395320a(10) =15308920a(11) =68213424a(12) =300999816a(13) =1317415792a(14) =5726300880a(15) =24742452128a(16) =106357582324a(17) =455122855224