Pascal's triangle, but the last element of the row is the sum of all the previous terms.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =3a(5) =8a(6) =1a(7) =4a(8) =11a(9) =32a(10) =1a(11) =5a(12) =15a(13) =43a(14) =128a(15) =1a(16) =6a(17) =20a(18) =58a(19) =171a(20) =512a(21) =1a(22) =7a(23) =26a(24) =78a(25) =229a(26) =683a(27) =2048a(28) =1a(29) =8