Augmentation of the triangle A008949. See Comments.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =5a(5) =8a(6) =1a(7) =9a(8) =30a(9) =44a(10) =1a(11) =14a(12) =77a(13) =212a(14) =296a(15) =1a(16) =20a(17) =163a(18) =700a(19) =1712a(20) =2312a(21) =1a(22) =27a(23) =305a(24) =1877a(25) =6882a(26) =15476a(27) =20384a(28) =1a(29) =35