Triangle read by rows: alternating binomial coefficients with signs.

Terms

a(0) =1a(1) =-4a(2) =1a(3) =15a(4) =-6a(5) =1a(6) =-56a(7) =28a(8) =-8a(9) =1a(10) =210a(11) =-120a(12) =45a(13) =-10a(14) =1a(15) =-792a(16) =495a(17) =-220a(18) =66a(19) =-12a(20) =1a(21) =3003a(22) =-2002a(23) =1001a(24) =-364a(25) =91a(26) =-14a(27) =1a(28) =-11440a(29) =8008