Augmentation of the triangular array P=A094727 given by p(n,k)=n+k+1 for 0<=k<=n. See Comments.

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =14a(5) =19a(6) =24a(7) =72a(8) =130a(9) =169a(10) =120a(11) =432a(12) =918a(13) =1482a(14) =1877a(15) =720a(16) =3000a(17) =7224a(18) =13140a(19) =19846a(20) =24675a(21) =5040a(22) =23760a(23) =63600a(24) =127104a(25) =210726a(26) =304006a(27) =372611a(28) =40320a(29) =211680