Augmentation of the triangle given by p(n,k)=(3+(-1)^k)/2 for 0<=k<=n. See Comments.

Terms

a(0) =1a(1) =2a(2) =1a(3) =4a(4) =4a(5) =5a(6) =8a(7) =12a(8) =22a(9) =17a(10) =16a(11) =32a(12) =72a(13) =88a(14) =89a(15) =32a(16) =80a(17) =208a(18) =328a(19) =474a(20) =417a(21) =64a(22) =192a(23) =560a(24) =1056a(25) =1836a(26) =2364a(27) =2253a(28) =128a(29) =448