a(n) = Sum_{k = 1..n} (-1)^(n+k) * k^3 * binomial(n,k)^2.

Terms

a(0) =0a(1) =1a(2) =4a(3) =-36a(4) =-96a(5) =450a(6) =1080a(7) =-3920a(8) =-8960a(9) =28350a(10) =63000a(11) =-182952a(12) =-399168a(13) =1093092a(14) =2354352a(15) =-6177600a(16) =-13178880a(17) =33474870a(18) =70887960a(19) =-175518200a(20) =-369512000a(21) =896251356a(22) =1877859984a(23) =-4478082336a(24) =-9345563136a(25) =21971267500a(26) =45700236400a(27) =-106148523600a(28) =-220159900800