a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026536.

Terms

a(0) =1a(1) =2a(2) =6a(3) =13a(4) =35a(5) =77a(6) =204a(7) =453a(8) =1199a(9) =2675a(10) =7089a(11) =15855a(12) =42070a(13) =94228a(14) =250269a(15) =561068a(16) =1491262a(17) =3345334a(18) =8896310a(19) =19966310a(20) =53118352a(21) =119257668a(22) =317373194a(23) =712742108a(24) =1897253203a(25) =4261711183a(26) =11346582851a(27) =25491926511a(28) =67882263130