a(n) = sum(sum(binomial(j-n-1,m),m=0..n),j=0..n).

Terms

a(0) =1a(1) =-1a(2) =7a(3) =-21a(4) =81a(5) =-295a(6) =1107a(7) =-4165a(8) =15793a(9) =-60171a(10) =230253a(11) =-884235a(12) =3406105a(13) =-13154947a(14) =50922987a(15) =-197519941a(16) =767502945a(17) =-2987013067a(18) =11641557717a(19) =-45429853651a(20) =177490745985a(21) =-694175171647