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

Terms

a(0) =1a(1) =4a(2) =16a(3) =104a(4) =572a(5) =2912a(6) =14720a(7) =73152a(8) =357648a(9) =1729216a(10) =8284928a(11) =39387008a(12) =186030016a(13) =873761792a(14) =4084183040a(15) =19010058240a(16) =88154661120a(17) =407447196672