a(n) = Sum{T(i,j)}, 0<=j<=i, 0<=i<=2n, T given by A026568.

Terms

a(0) =1a(1) =4a(2) =11a(3) =30a(4) =77a(5) =200a(6) =511a(7) =1314a(8) =3361a(9) =8620a(10) =22067a(11) =56550a(12) =144821a(13) =371024a(14) =950311a(15) =2434410a(16) =6235657a(17) =15973300a(18) =40915931a(19) =104809134a(20) =268472861a(21) =687709400a(22) =1761600847a(23) =4512438450a(24) =11558841841a(25) =29608595644a(26) =75843963011