a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)^2.

Terms

a(0) =1a(1) =1a(2) =5a(3) =10a(4) =53a(5) =126a(6) =662a(7) =1716a(8) =8885a(9) =24310a(10) =124130a(11) =352716a(12) =1778966a(13) =5200300a(14) =25947612a(15) =77558760a(16) =383358645a(17) =1166803110a(18) =5719519850a(19) =17672631900a(20) =85990654178a(21) =269128937220