a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026769.

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =14a(5) =26a(6) =70a(7) =138a(8) =362a(9) =742a(10) =1912a(11) =4028a(12) =10249a(13) =22033a(14) =55547a(15) =121273a(16) =303641a(17) =670997a(18) =1671233a(19) =3729071a(20) =9250099a(21) =20803231a(22) =51437219a(23) =116436313a(24) =287152067a(25) =653567143a(26) =1608416195a(27) =3677760541a(28) =9035150126a(29) =20741496354