Triangle read by rows: row n is the expansion of x^n in terms of (x+k)!/x! for decreasing k.

Terms

a(0) =1a(1) =1a(2) =-1a(3) =1a(4) =-3a(5) =1a(6) =1a(7) =-6a(8) =7a(9) =-1a(10) =1a(11) =-10a(12) =25a(13) =-15a(14) =1a(15) =1a(16) =-15a(17) =65a(18) =-90a(19) =31a(20) =-1a(21) =1a(22) =-21a(23) =140a(24) =-350a(25) =301a(26) =-63a(27) =1a(28) =1a(29) =-28