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Array T by antidiagonals, T(k,n)=(k+1)*n*2^(n-1)+1, n >= 0, k >= 1.
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%I #7 Jun 13 2017 02:16:51

%S 1,2,1,5,3,1,13,9,4,1,33,25,13,5,1,81,65,37,17,6,1,193,161,97,49,21,7,

%T 1,449,385,241,129,61,25,8,1,1025,897,577,321,161,73,29,9,1,2305,2049,

%U 1345,769,401,193,85,33,10,1,5121,4609,3073

%N Array T by antidiagonals, T(k,n)=(k+1)*n*2^(n-1)+1, n >= 0, k >= 1.

%C n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is (k+1)n, for n=1,2,3,...; k=0,1,2,...

%e Antidiagonals: {1}; {2,1}; {5,3,1}; ...

%o (PARI) T(n,k)=if(n<0 || k<1,0,k*n*2^(n-1)+1)

%Y See A049069 for transposed array.

%Y Row 1 = (1, 2, 5, 13, 33, ...) = A005183.

%Y Row 2 = (1, 3, 9, 25, 65, ...) = A002064.

%K nonn,tabl,easy

%O 0,2

%A _Clark Kimberling_

%E Better description from Michael Somos