a(n) = sum_{k = 0..n-1} (-1)^k*C(2*n-1,k)*C(n-1,k), n>0.

Terms

a(0) =1a(1) =-2a(2) =1a(3) =8a(4) =-29a(5) =34a(6) =92a(7) =-512a(8) =919a(9) =818a(10) =-9151a(11) =22472a(12) =-2924a(13) =-156872a(14) =513736a(15) =-443392a(16) =-2457281a(17) =11094658a(18) =-16502221a(19) =-31859752a(20) =226433243a(21) =-475853006a(22) =-217535264a(23) =4333621888a(24) =-12126499804a(25) =5346234424