a(n) = binomial(2n+1, n+1) - 1.

Terms

a(0) =0a(1) =2a(2) =9a(3) =34a(4) =125a(5) =461a(6) =1715a(7) =6434a(8) =24309a(9) =92377a(10) =352715a(11) =1352077a(12) =5200299a(13) =20058299a(14) =77558759a(15) =300540194a(16) =1166803109a(17) =4537567649a(18) =17672631899a(19) =68923264409a(20) =269128937219