a(n) = Sum{T(i,j)}, 0<=j<=i, 0<=i<=n, T given by A026552.

Terms

a(0) =1a(1) =3a(2) =9a(3) =20a(4) =53a(5) =117a(6) =308a(7) =684a(8) =1806a(9) =4028a(10) =10664a(11) =23844a(12) =63239a(13) =141612a(14) =376026a(15) =842866a(16) =2239900a(17) =5024166a(18) =13359408a(19) =29980384a(20) =79753402a(21) =179044760a(22) =476451644a(23) =1069936084a(24) =2847931619a(25) =6396900694a(26) =17030741437a(27) =38260956765