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A205548 Symmetric matrix by antidiagonals: C(max(i+1,j+1),min(i+1,j+1)), i>=1, j>=1.

%I A205548 #5 Mar 30 2012 18:58:11
%S A205548 1,3,3,6,1,6,10,4,4,10,15,10,1,10,15,21,20,5,5,20,21,28,35,15,1,15,35,
%T A205548 28,36,56,35,6,6,35,56,36,45,84,70,21,1,21,70,84,45,55,120,126,56,7,7,
%U A205548 56,126,120,55,66,165,210,126,28,1,28,126,210,165,66,78,220
%N A205548 Symmetric matrix by antidiagonals:  C(max(i+1,j+1),min(i+1,j+1)), i>=1, j>=1.
%e A205548 Northwest corner:
%e A205548 1....3....6....10...15
%e A205548 3....1....4....10...20
%e A205548 6....4....1....5....15
%e A205548 10...10...5....1....6
%e A205548 15...20...15...6....1
%t A205548 g[k_] := k + 1;
%t A205548 f[i_, j_] := Binomial[Max[g[i], g[j]], Min[g[i], g[j]]]
%t A205548 TableForm[Table[f[i, j], {i, 1, 10}, {j, 1, 10}]]
%t A205548 Flatten[Table[f[i, n + 1 - i], {n, 1, 14}, {i, 1, n}]]
%Y A205548 Cf. A205456.
%K A205548 nonn,tabl
%O A205548 1,2
%A A205548 _Clark Kimberling_, Jan 28 2012