Triangle by columns: A013610 signed and interleaved with zeros.

Terms

a(0) =1a(1) =0a(2) =3a(3) =-1a(4) =0a(5) =9a(6) =0a(7) =-6a(8) =0a(9) =27a(10) =1a(11) =0a(12) =-27a(13) =0a(14) =81a(15) =0a(16) =9a(17) =0a(18) =-108a(19) =0a(20) =243a(21) =-1a(22) =0a(23) =54a(24) =0a(25) =-405a(26) =0a(27) =729a(28) =0a(29) =-12