Eigentriangle, row sums = A125275.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =2a(6) =5a(7) =9a(8) =10a(9) =7a(10) =14a(11) =28a(12) =40a(13) =49a(14) =31a(15) =42a(16) =90a(17) =150a(18) =245a(19) =279a(20) =162a(21) =132a(22) =297a(23) =550a(24) =1078a(25) =1674a(26) =1782a(27) =968a(28) =429a(29) =1001