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Array T read by diagonals; n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is (k+2)^(n-1), for n=1,2,3,...; k=0,1,2,...
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%I #10 Jun 16 2023 09:45:33

%S 1,2,1,5,2,1,14,6,2,1,41,22,7,2,1,122,86,32,8,2,1,365,342,157,44,9,2,

%T 1,1094,1366,782,260,58,10,2,1,3281,5462,3907,1556,401,74,11,2,1,9842,

%U 21846,19532,9332,2802,586,92,12,2,1,29525,87382

%N Array T read by diagonals; n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is (k+2)^(n-1), for n=1,2,3,...; k=0,1,2,...

%F T(k, n) = ((k+3)^n+k+1)/(k+2). - _Ralf Stephan_, Feb 14 2004

%e Diagonals (each starting on row 1): {1}; {2,1}; {5,2,1}; ...

%Y Row 1 = (1, 2, 5, 14, 41, ...) = A007051.

%Y Row 2 = (1, 2, 6, 22, 86, ...) = A047849.

%Y Row 3 = (1, 2, 7, 32, 157, ...) = A047850.

%Y Row 4 = (1, 2, 8, 44, 260, ...) = A047851.

%Y Row 5 = (1, 2, 9, 58, 401, ...) = A047852.

%Y Row 6 = (1, 2, 10, 74, 586, ...) = A047853.

%Y Row 7 = (1, 2, 11, 92, 821, ...) = A047854.

%Y Row 8 = (1, 2, 12, 112, 1112, ...) = A047855.

%Y Row 9 = (1, 2, 13, 134, 1465, ...) = A047856.

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_