a(n) = (2^n + C(2*n,n))/2.

Terms

a(0) =1a(1) =2a(2) =5a(3) =14a(4) =43a(5) =142a(6) =494a(7) =1780a(8) =6563a(9) =24566a(10) =92890a(11) =353740a(12) =1354126a(13) =5204396a(14) =20066492a(15) =77575144a(16) =300572963a(17) =1166868646a(18) =4537698722a(19) =17672894044a(20) =68923788698a(21) =269129985796