Number of n-element subsets of [2n] having an even sum.

Terms

a(0) =1a(1) =1a(2) =2a(3) =10a(4) =38a(5) =126a(6) =452a(7) =1716a(8) =6470a(9) =24310a(10) =92252a(11) =352716a(12) =1352540a(13) =5200300a(14) =20056584a(15) =77558760a(16) =300546630a(17) =1166803110a(18) =4537543340a(19) =17672631900a(20) =68923356788a(21) =269128937220