a(n) is the number of odd-balanced unimodal sequences of weight 2n+2.

Terms

a(0) =1a(1) =2a(2) =5a(3) =9a(4) =16a(5) =29a(6) =48a(7) =77a(8) =123a(9) =191a(10) =290a(11) =436a(12) =643a(13) =936a(14) =1352a(15) =1927a(16) =2720a(17) =3810a(18) =5287a(19) =7282a(20) =9965a(21) =13539a(22) =18280a(23) =24545a(24) =32769a(25) =43519a(26) =57522a(27) =75667a(28) =99092a(29) =129237