a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026780.

Terms

a(0) =1a(1) =3a(2) =8a(3) =19a(4) =45a(5) =103a(6) =239a(7) =545a(8) =1262a(9) =2887a(10) =6700a(11) =15397a(12) =35848a(13) =82757a(14) =193320a(15) =448175a(16) =1050217a(17) =2443963a(18) =5743267a(19) =13410053a(20) =31593029a(21) =73984575a(22) =174689181a(23) =410141597a(24) =970289011a(25) =2283205051a(26) =5410611863a(27) =12756825609a(28) =30274963923