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