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A083064 Square number array T(n,k) = (k*(k+2)^n+1)/(k+1) read by antidiagonals.

%I A083064 #9 Jan 25 2023 16:43:10
%S A083064 1,1,1,1,2,1,1,3,5,1,1,4,11,14,1,1,5,19,43,41,1,1,6,29,94,171,122,1,1,
%T A083064 7,41,173,469,683,365,1,1,8,55,286,1037,2344,2731,1094,1,1,9,71,439,
%U A083064 2001,6221,11719,10923,3281,1,1,10,89,638,3511,14006,37325,58594,43691,9842,1
%N A083064 Square number array T(n,k) = (k*(k+2)^n+1)/(k+1) read by antidiagonals.
%e A083064 Rows begin:
%e A083064 1  1   1    1     1      1       1        1         1 ...
%e A083064 1  2   5   14    41    122     365     1094      3281 ...  A007051
%e A083064 1  3  11   43   171    683    2731    10923     43691 ...  A007583
%e A083064 1  4  19   94   469   2344   11719    58594    292969 ...  A083065
%e A083064 1  5  29  173  1037   6221   37325   223949   1343693 ...  A083066
%e A083064 1  6  41  286  2001  14006   98041   686286   4804001 ...  A083067
%e A083064 1  7  55  439  3511  28087  224695  1797559  14380471 ...  A083068
%e A083064 1  8  71  638  5741  51668  465011  4185098  37665881 ...  A187709
%e A083064 1  9  89  889  8889  88889  888889  8888889  88888889 ...  A059482
%e A083064 1 10 109 1198 13177 144946 1594405 17538454 192922993 ...  A199760, etc.
%e A083064 Column 2: A000027;
%e A083064 column 3: A028387;
%e A083064 column 4: A083074;
%e A083064 column 5: A125082;
%e A083064 column 6: A125083.
%e A083064 Diagonals:
%e A083064 1,  2,  11,   94,  1037,  14006, ... A083069;
%e A083064 1,  3,  19,  173,  2001,  28087, ... A083071;
%e A083064 1,  4,  29,  286,  3511,  51668, ... A083072;
%e A083064 1,  5,  41,  439,  5741,  88889, ... A083073;
%e A083064 1,  5,  43,  469,  6221,  98041, ... A083070;
%e A083064 1, 14, 171, 2344, 37325, 686286, ... A191690.
%e A083064 Triangle begins:
%e A083064 1;
%e A083064 1, 1;
%e A083064 1, 2, 1;
%e A083064 1, 3, 5, 1;
%e A083064 1, 4, 11, 14, 1;
%e A083064 1, 5, 19, 43, 41, 1;
%e A083064 1, 6, 29, 94, 171, 122, 1; etc.
%Y A083064 Cf. rows: A007051, A007583, A059482, A083065 - A083068, A187709, A199760; columns:  A000027, A028387, A083074, A125082, A125083; diagonals: A083069 - A083073, A191690.
%K A083064 nonn,easy,tabl
%O A083064 0,5
%A A083064 _Paul Barry_, Apr 21 2003
%E A083064 Edited by _Bruno Berselli_, Jun 21 2013