a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026747.

Terms

a(0) =1a(1) =3a(2) =8a(3) =18a(4) =42a(5) =90a(6) =204a(7) =432a(8) =972a(9) =2052a(10) =4610a(11) =9726a(12) =21859a(13) =46125a(14) =103783a(15) =219099a(16) =493699a(17) =1042899a(18) =2353716a(19) =4975350a(20) =11247138a(21) =23790714a(22) =53867343a(23) =114020601a(24) =258571256a(25) =547672566a(26) =1243848888a(27) =2636201532a(28) =5995717860