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

Terms

a(0) =1a(1) =1a(2) =-3a(3) =-2a(4) =21a(5) =-4a(6) =-150a(7) =155a(8) =1029a(9) =-2072a(10) =-6468a(11) =22056a(12) =34122a(13) =-208857a(14) =-106249a(15) =1816958a(16) =-639067a(17) =-14629264a(18) =17635800a(19) =108117620a(20) =-239571684a(21) =-711876496a(22) =2628772968a(23) =3825823888a(24) =-25582846134a(25) =-10997156129a(26) =227594431035a(27) =-98360217830