Augmentation of the Euler triangle A008292. See Comments.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =5a(5) =2a(6) =1a(7) =16a(8) =33a(9) =8a(10) =1a(11) =42a(12) =275a(13) =342a(14) =58a(15) =1a(16) =99a(17) =1669a(18) =6441a(19) =5600a(20) =718a(21) =1a(22) =219a(23) =8503a(24) =82149a(25) =217694a(26) =143126a(27) =14528a(28) =1a(29) =466