a(n) = Sum_{k=0..n} T(n,k), T given by A026769.

Terms

a(0) =1a(1) =2a(2) =4a(3) =9a(4) =19a(5) =43a(6) =93a(7) =212a(8) =466a(9) =1070a(10) =2382a(11) =5506a(12) =12386a(13) =28800a(14) =65356a(15) =152745a(16) =349183a(17) =819639a(18) =1885361a(19) =4441719a(20) =10270279a(21) =24269629a(22) =56363319a(23) =133529869a(24) =311255601a(25) =738947515a(26) =1727873793a(27) =4109314729a(28) =9634406661a(29) =22946573863