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

Terms

a(0) =1a(1) =-3a(2) =8a(3) =-30a(4) =128a(5) =-518a(6) =2048a(7) =-8172a(8) =32768a(9) =-131142a(10) =524288a(11) =-2096900a(12) =8388608a(13) =-33555356a(14) =134217728a(15) =-536867480a(16) =2147483648a(17) =-8589947462a(18) =34359738368a(19) =-137438904852a(20) =549755813888