a(n) = Sum_{k=0..n} T(n,k), T given by A026780.

Terms

a(0) =1a(1) =2a(2) =5a(3) =11a(4) =26a(5) =58a(6) =136a(7) =306a(8) =717a(9) =1625a(10) =3813a(11) =8697a(12) =20451a(13) =46909a(14) =110563a(15) =254855a(16) =602042a(17) =1393746a(18) =3299304a(19) =7666786a(20) =18182976a(21) =42391546a(22) =100704606a(23) =235452416a(24) =560147414a(25) =1312916040a(26) =3127406812a(27) =7346213746a(28) =17518138314a(29) =41228281888