a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026769.

Terms

a(0) =1a(1) =3a(2) =7a(3) =16a(4) =35a(5) =78a(6) =171a(7) =383a(8) =849a(9) =1919a(10) =4301a(11) =9807a(12) =22193a(13) =50993a(14) =116349a(15) =269094a(16) =618277a(17) =1437916a(18) =3323277a(19) =7764996a(20) =18035275a(21) =42304904a(22) =98668223a(23) =232198092a(24) =543453693a(25) =1282401208a(26) =3010275001a(27) =7119589730a(28) =16753996391