a(n) = Sum_{k=0..n} binomial(n, 2k)*binomial(n-k, k)*(-1)^k.

Terms

a(0) =1a(1) =1a(2) =0a(3) =-5a(4) =-16a(5) =-24a(6) =15a(7) =197a(8) =576a(9) =724a(10) =-1200a(11) =-8832a(12) =-22801a(13) =-21293a(14) =76440a(15) =408795a(16) =922368a(17) =499104a(18) =-4446588a(19) =-19025060a(20) =-37012416a(21) =-1673992a(22) =245604832a(23) =880263936a(24) =1441226991a(25) =-908700649a(26) =-13088509200a(27) =-40222012703a(28) =-52991533744a(29) =88167061704