%I A080853
%S A080853 1,1,1,1,2,1,1,3,4,1,1,4,9,7,1,1,5,16,19,11,1,1,6,25,37,33,16,1,1,7,36,
%T A080853 61,67,51,22,1,1,8,49,91,113,106,73,29,1,1,9,64,127,171,181,154,99,37,
               1,
%U A080853 1,10,81,169,241,276,265,211,129,46,1,1,11,100,217,323,391,406,365,277
%N A080853 Square array of generalized polygonal numbers, read by antidiagonals.
%F A080853 T(n, k)=C(k, 0)+C(k, 1)n+C(k, 2)n^2=(n^2*k^2-(n^2-2n)*k+2)/2 =(k(k-1)*n^2+2k*n+2)/
               2 Row n has g.f. (1+(n-2)x+(n^2-n+1)x^2)/(1-x)^3. Column k has g.f. 
               (C(k-1, 0)+(C(k+1, 2)-2)*x+C(k-1, 2)*x^2)/(1-x)^3. Diagonals are 
               given by (n^4+(2k-1)*n^3+((k-1)^2+1)*n^2+(1-(k-1)^2)*n+2)/2
%e A080853 Rows begin
%e A080853 1 1 1 1 1 ...
%e A080853 1 2 4 7 11 ...
%e A080853 1 3 9 19 33 ...
%e A080853 1 4 16 37 67 ...
%e A080853 1 5 25 61 113 ...
%Y A080853 Rows include A000124, A058331, A080855, A080856, A080857, A080919.
%Y A080853 Columns include A000290, A003215, A003215, A080859, A080860, A080861.
%Y A080853 Sequence in context: A144042 A122084 A104559 this_sequence A071922 A138028 
               A009999
%Y A080853 Adjacent sequences: A080850 A080851 A080852 this_sequence A080854 A080855 
               A080856
%K A080853 easy,nonn,tabl
%O A080853 0,5
%A A080853 Paul Barry (pbarry(AT)wit.ie), Feb 23 2003