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

Terms

a(0) =-1a(1) =-1a(2) =1a(3) =5a(4) =13a(5) =29a(6) =63a(7) =139a(8) =317a(9) =749a(10) =1827a(11) =4575a(12) =11699a(13) =30419a(14) =80161a(15) =213573a(16) =574253a(17) =1556077a(18) =4244835a(19) =11647151a(20) =32122231a(21) =88995879a(22) =247573565a(23) =691246369a(24) =1936445619a(25) =5441165699a(26) =15331341373a(27) =43308322049a(28) =122624939677a(29) =347957102909