Riordan array (1-u, u) where u=(-1 + sqrt(1+8*x))/4.

Terms

a(0) =1a(1) =-1a(2) =1a(3) =2a(4) =-3a(5) =1a(6) =-8a(7) =12a(8) =-5a(9) =1a(10) =40a(11) =-60a(12) =26a(13) =-7a(14) =1a(15) =-224a(16) =336a(17) =-148a(18) =44a(19) =-9a(20) =1a(21) =1344a(22) =-2016a(23) =896a(24) =-280a(25) =66a(26) =-11a(27) =1a(28) =-8448a(29) =12672