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A205550 Symmetric matrix by antidiagonals: C(max(g(i),g(j)),min(g(i),g(j))), where g(k)=2k-1.

%I A205550 #7 Dec 25 2023 18:14:55
%S A205550 1,3,3,5,1,5,7,10,10,7,9,35,1,35,9,11,84,21,21,84,11,13,165,126,1,126,
%T A205550 165,13,15,286,462,36,36,462,286,15,17,455,1287,330,1,330,1287,455,17,
%U A205550 19,680,3003,1716,55,55,1716,3003,680,19,21,969,6188,6435,715
%N A205550 Symmetric matrix by antidiagonals: C(max(g(i),g(j)),min(g(i),g(j))), where g(k)=2k-1.
%e A205550 Northwest corner:
%e A205550 1....3....5....7....9....11
%e A205550 3....1....10...35...84...165
%e A205550 5....10...1....21...126..462
%e A205550 7....35...21...1....36...330
%t A205550 g[k_] := 2 k - 1;
%t A205550 f[i_, j_] := Binomial[Max[g[i], g[j]], Min[g[i], g[j]]]
%t A205550 TableForm[Table[f[i, j], {i, 1, 10}, {j, 1, 10}]]
%t A205550 Flatten[Table[f[i, n + 1 - i], {n, 1, 14}, {i, 1, n}]]
%Y A205550 Cf. A205456.
%K A205550 nonn,tabl
%O A205550 1,2
%A A205550 _Clark Kimberling_, Jan 28 2012