a(n) = 4^n*binomial(n - 1/2, -1/2)*(n^2 + 1).

Terms

a(0) =1a(1) =4a(2) =30a(3) =200a(4) =1190a(5) =6552a(6) =34188a(7) =171600a(8) =836550a(9) =3986840a(10) =18660356a(11) =86062704a(12) =392102620a(13) =1768102000a(14) =7902970200a(15) =35056559520a(16) =154477660230a(17) =676745803800