a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026519.

Terms

a(0) =1a(1) =3a(2) =7a(3) =18a(4) =40a(5) =104a(6) =231a(7) =607a(8) =1353a(9) =3575a(10) =7989a(11) =21169a(12) =47384a(13) =125757a(14) =281798a(15) =748638a(16) =1678832a(17) =4463098a(18) =10014074a(19) =26635050a(20) =59787092a(21) =159078450a(22) =357193976a(23) =950678416a(24) =2135189511a(25) =5684158586a(26) =12769030254a(27) =33999245582