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A175990 Irregular triangle read by rows: t(n,m) = binomial(n-m-1,m+1) for 0 <= m <= floor((n-1)/2).

%I A175990 #24 Mar 25 2024 07:53:53
%S A175990 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 A175990 36,56,35,6,0,11,45,84,70,21,1,12,55,120,126,56,7,0,13,66,165,210,126,
%U A175990 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 A175990 Irregular triangle read by rows: t(n,m) = binomial(n-m-1,m+1) for 0 <= m <= floor((n-1)/2).
%e A175990 Triangle begins:
%e A175990    1;
%e A175990    2,  0;
%e A175990    3,  1;
%e A175990    4,  3,  0;
%e A175990    5,  6,  1;
%e A175990    6, 10,  4,  0;
%e A175990    7, 15, 10,  1;
%e A175990    8, 21, 20,  5,  0;
%e A175990    9, 28, 35, 15,  1;
%e A175990   10, 36, 56, 35,  6,  0;
%e A175990   11, 45, 84, 70, 21,  1;
%t A175990 Table[Binomial[n-m-1,m+1],{n,2,15},{m,0,Floor[(n-1)/2]}]//Flatten (* _Harvey P. Dale_, May 08 2023 *)
%Y A175990 Row sums are A000071.
%Y A175990 Essentially the same as A011973 (removing first column). Elimination of each 2nd row yields essentially A054142 or A121314. Interleaving with zeros gives A052553.
%Y A175990 Padding with an initial column of 1's and more zeros yields A169803. Signed variants are A115139 and A124033.
%K A175990 nonn,tabf,easy,less
%O A175990 2,2
%A A175990 _Roger L. Bagula_, Dec 06 2010
%E A175990 Definition clarified by _Harvey P. Dale_, May 08 2023