a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027052.

Terms

a(0) =1a(1) =1a(2) =4a(3) =22a(4) =93a(5) =389a(6) =1570a(7) =6144a(8) =23629a(9) =89551a(10) =335430a(11) =1244762a(12) =4583293a(13) =16765087a(14) =60980096a(15) =220724896a(16) =795540601a(17) =2856541663a(18) =10222762962a(19) =36475315442a(20) =129796579409a(21) =460757642587