a(n) = Sum_{k=0..m} (k+1) * A026148(n, m-k), where m=0 for n=1; m=n+1 for n >= 2.

Terms

a(0) =1a(1) =3a(2) =18a(3) =54a(4) =162a(5) =486a(6) =1458a(7) =4374a(8) =13122a(9) =39366a(10) =118098a(11) =354294a(12) =1062882a(13) =3188646a(14) =9565938a(15) =28697814a(16) =86093442a(17) =258280326a(18) =774840978a(19) =2324522934a(20) =6973568802a(21) =20920706406a(22) =62762119218a(23) =188286357654a(24) =564859072962