a(n) = T(n, floor(n/2)), T given by A026780.

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =12a(5) =24a(6) =53a(7) =117a(8) =246a(9) =580a(10) =1178a(11) =2916a(12) =5768a(13) =14834a(14) =28731a(15) =76221a(16) =145108a(17) =395048a(18) =741392a(19) =2063104a(20) =3825418a(21) =10847078a(22) =19907156a(23) =57373672a(24) =104370554a(25) =305110106a(26) =550816506a(27) =1630489090a(28) =2924018194a(29) =8751851866