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A216916 Triangle read by rows, T(n,k) for 0<=k<=n, generalizing A098742.

%I A216916 #15 Mar 17 2020 14:21:25
%S A216916 1,1,1,3,3,1,9,12,6,1,33,51,34,10,1,135,237,193,79,15,1,609,1188,1132,
%T A216916 584,160,21,1,2985,6381,6920,4268,1510,293,28,1,15747,36507,44213,
%U A216916 31542,13576,3464,497,36,1,88761,221400,295314,238261,120206,37839,7231,794
%N A216916 Triangle read by rows, T(n,k) for 0<=k<=n, generalizing A098742.
%C A216916 Full concordance with A098742 would require two zero rows at the top of the triangle which we omitted for simplicity.
%C A216916 Matrix inverse is A137338. - _Peter Luschny_, Sep 21 2012
%F A216916 Recurrence: T(0,0)=1, T(0,k)=0 for k>0 and for n>=1 T(n,k) = T(n-1,k-1) + (k+1)*T(n-1,k) + (k+2)*T(n-1,k+1).
%e A216916 [0] [1]
%e A216916 [1] [1, 1]
%e A216916 [2] [3, 3, 1]
%e A216916 [3] [9, 12, 6, 1]
%e A216916 [4] [33, 51, 34, 10, 1]
%e A216916 [5] [135, 237, 193, 79, 15, 1]
%e A216916 [6] [609, 1188, 1132, 584, 160, 21, 1]
%e A216916 [7] [2985, 6381, 6920, 4268, 1510, 293, 28, 1]
%e A216916 [8] [15747, 36507, 44213, 31542, 13576, 3464, 497, 36, 1]
%o A216916 (Sage)
%o A216916 def A216916_triangle(dim):
%o A216916     T = matrix(ZZ,dim,dim)
%o A216916     for n in range(dim): T[n,n] = 1
%o A216916     for n in (1..dim-1):
%o A216916         for k in (0..n-1):
%o A216916             T[n,k] = T[n-1,k-1]+(k+1)*T[n-1,k]+(k+2)*T[n-1,k+1]
%o A216916     return T
%o A216916 A216916_triangle(9)
%K A216916 nonn,tabl
%O A216916 0,4
%A A216916 _Peter Luschny_, Sep 20 2012