a(n) = Sum_{k=floor((n+2)/2)..n} T(n, k), T given by A026998.

Terms

a(0) =1a(1) =1a(2) =9a(3) =14a(4) =46a(5) =81a(6) =209a(7) =389a(8) =901a(9) =1726a(10) =3774a(11) =7349a(12) =15541a(13) =30561a(14) =63329a(15) =125294a(16) =256366a(17) =509161a(18) =1033449a(19) =2057549a(20) =4154701a(21) =8284926a(22) =16673534a(23) =33282989a(24) =66837421a(25) =133507081a(26) =267724809a(27) =535010414a(28) =1071881326a(29) =2142612801