Triangle: p(x) = (t/log(1 + t))^a0*(1 + t)^x; a0=2; weights (n+1)!*n!.

Terms

a(0) =1a(1) =2a(2) =2a(3) =1a(4) =6a(5) =6a(6) =0a(7) =-12a(8) =0a(9) =24a(10) =-12a(11) =120a(12) =0a(13) =-240a(14) =120a(15) =360a(16) =-2280a(17) =0a(18) =4800a(19) =-3600a(20) =720a(21) =-13260a(22) =68040a(23) =0a(24) =-151200a(25) =138600a(26) =-45360a(27) =5040a(28) =638400a(29) =-2899680