Sum of heights of all 1-watermelons with wall of length 2*n.

Terms

a(0) =1a(1) =3a(2) =10a(3) =34a(4) =118a(5) =417a(6) =1495a(7) =5421a(8) =19838a(9) =73149a(10) =271453a(11) =1012872a(12) =3797228a(13) =14294518a(14) =54006728a(15) =204702328a(16) =778115558a(17) =2965409556a(18) =11327549778a(19) =43361526366a(20) =166306579062a(21) =638969153207