Diagonal sums of a sum-of-powers triangle.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =8a(6) =14a(7) =26a(8) =53a(9) =117a(10) =280a(11) =721a(12) =1989a(13) =5844a(14) =18188a(15) =59652a(16) =205305a(17) =739041a(18) =2775190a(19) =10846975a(20) =44039765a(21) =185391480a(22) =807776210a(23) =3637193486a(24) =16900721837a(25) =80939650565a(26) =399061251260