a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026584.

Terms

a(0) =1a(1) =2a(2) =6a(3) =14a(4) =37a(5) =91a(6) =234a(7) =588a(8) =1502a(9) =3808a(10) =9715a(11) =24727a(12) =63095a(13) =160899a(14) =410764a(15) =1048598a(16) =2678327a(17) =6841725a(18) =17482478a(19) =44678724a(20) =114205286a(21) =291963048a(22) =746504245a(23) =1908907425a(24) =4881860810a(25) =12486083994a(26) =31937825727a(27) =81699259367