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

Terms

a(0) =1a(1) =10a(2) =126a(3) =1716a(4) =24310a(5) =352716a(6) =5200300a(7) =77558760a(8) =1166803110a(9) =17672631900a(10) =269128937220