Augmentation of the triangular array P given by p(n,k)=k! for 0<=k<=n. See Comments.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =1a(7) =3a(8) =7a(9) =13a(10) =1a(11) =4a(12) =12a(13) =32a(14) =69a(15) =1a(16) =5a(17) =18a(18) =58a(19) =173a(20) =421a(21) =1a(22) =6a(23) =25a(24) =92a(25) =321a(26) =1058a(27) =2867a(28) =1a(29) =7