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

Terms

a(0) =1a(1) =-1a(2) =3a(3) =-10a(4) =35a(5) =-126a(6) =462a(7) =-1716a(8) =6435a(9) =-24310a(10) =92378a(11) =-352716a(12) =1352078a(13) =-5200300a(14) =20058300a(15) =-77558760a(16) =300540195a(17) =-1166803110a(18) =4537567650a(19) =-17672631900a(20) =68923264410a(21) =-269128937220