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A205553 Square array by antidiagonals: C(max(i-1,2j-2),min(i-1,2j-2)), i>=1, j>=1.

%I A205553 #8 Jul 03 2020 14:55:05
%S A205553 1,1,1,1,2,1,1,4,1,1,1,6,6,3,1,1,8,15,4,6,1,1,10,28,20,1,10,1,1,12,45,
%T A205553 56,15,5,15,1,1,14,66,120,70,6,15,21,1,1,16,91,220,210,56,1,35,28,1,1,
%U A205553 18,120,364,495,252,28,7,70,36,1,1,20,153,560,1001,792,210,8
%N A205553 Square array by antidiagonals: C(max(i-1,2j-2),min(i-1,2j-2)), i>=1, j>=1.
%H A205553 Milan Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Janjic/janjic73.html">Binomial Coefficients and Enumeration of Restricted Words</a>, Journal of Integer Sequences, 2016, Vol 19, #16.7.3
%e A205553 Northwest corner:
%e A205553 1....1....1....1....1
%e A205553 1....2....4....6....8
%e A205553 1....1....6....15...28
%e A205553 1....3....4....20...56
%e A205553 1....6....1....15...70
%t A205553 f[i_, j_] := Binomial[Max[i - 1, 2 j - 2], Min[i - 1, 2 j - 2]]
%t A205553 TableForm[Table[f[i, j], {i, 1, 10}, {j, 1, 10}]]
%t A205553 Flatten[Table[f[i, n + 1 - i], {n, 1, 14}, {i, 1, n}]]
%Y A205553 Cf. A205456.
%K A205553 nonn,tabl
%O A205553 1,5
%A A205553 _Clark Kimberling_, Jan 28 2012