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%I #24 Mar 25 2024 07:53:53
%S 1,2,0,3,1,4,3,0,5,6,1,6,10,4,0,7,15,10,1,8,21,20,5,0,9,28,35,15,1,10,
%T 36,56,35,6,0,11,45,84,70,21,1,12,55,120,126,56,7,0,13,66,165,210,126,
%U 28,1,14,78,220,330,252,84,8,0,15,91,286,495,462,210,36,1,16,105,364,715,792,462,120,9,0,17,120
%N Irregular triangle read by rows: t(n,m) = binomial(n-m-1,m+1) for 0 <= m <= floor((n-1)/2).
%e Triangle begins:
%e 1;
%e 2, 0;
%e 3, 1;
%e 4, 3, 0;
%e 5, 6, 1;
%e 6, 10, 4, 0;
%e 7, 15, 10, 1;
%e 8, 21, 20, 5, 0;
%e 9, 28, 35, 15, 1;
%e 10, 36, 56, 35, 6, 0;
%e 11, 45, 84, 70, 21, 1;
%t Table[Binomial[n-m-1,m+1],{n,2,15},{m,0,Floor[(n-1)/2]}]//Flatten (* _Harvey P. Dale_, May 08 2023 *)
%Y Row sums are A000071.
%Y Essentially the same as A011973 (removing first column). Elimination of each 2nd row yields essentially A054142 or A121314. Interleaving with zeros gives A052553.
%Y Padding with an initial column of 1's and more zeros yields A169803. Signed variants are A115139 and A124033.
%K nonn,tabf,easy,less
%O 2,2
%A _Roger L. Bagula_, Dec 06 2010
%E Definition clarified by _Harvey P. Dale_, May 08 2023
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