a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(2*n-2*k+1,2*k+1).

Terms

a(0) =1a(1) =3a(2) =7a(3) =27a(4) =83a(5) =263a(6) =855a(7) =2723a(8) =8731a(9) =27999a(10) =89663a(11) =287355a(12) =920771a(13) =2950263a(14) =9453607a(15) =30291667a(16) =97062123a(17) =311012623a(18) =996563855a(19) =3193247403a(20) =10231988371a(21) =32785923879a(22) =105054547063a(23) =336621829635