a(n) = Sum_{k=0..m} (k+1) * A026120(n, m-k), where m=0 for n=0,1; m=n for n >= 2.

Terms

a(0) =1a(1) =3a(2) =12a(3) =36a(4) =108a(5) =324a(6) =972a(7) =2916a(8) =8748a(9) =26244a(10) =78732a(11) =236196a(12) =708588a(13) =2125764a(14) =6377292a(15) =19131876a(16) =57395628a(17) =172186884a(18) =516560652a(19) =1549681956a(20) =4649045868a(21) =13947137604a(22) =41841412812a(23) =125524238436a(24) =376572715308