A177040 Irregular triangle t(n,m) = binomial(m+1,n-m) read by rows floor((n+1)/2) <= m <= n.
1, 1, 2, 1, 3, 1, 3, 4, 1, 6, 5, 1, 4, 10, 6, 1, 10, 15, 7, 1, 5, 20, 21, 8, 1, 15, 35, 28, 9, 1, 6, 35, 56, 36, 10, 1, 21, 70, 84, 45, 11, 1, 7, 56, 126, 120, 55, 12, 1, 28, 126, 210, 165, 66, 13, 1, 8, 84, 252, 330, 220, 78, 14, 1, 36, 210, 462, 495, 286, 91, 15, 1
Offset: 0
Examples
1; 1; 2, 1; 3, 1; 3, 4, 1; 6, 5, 1; 4, 10, 6, 1; 10, 15, 7, 1; 5, 20, 21, 8, 1; 15, 35, 28, 9, 1; 6, 35, 56, 36, 10, 1; 21, 70, 84, 45, 11, 1; 7, 56, 126, 120, 55, 12, 1; 28, 126, 210, 165, 66, 13, 1; 8, 84, 252, 330, 220, 78, 14, 1; 36, 210, 462, 495, 286, 91, 15, 1;
Programs
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Mathematica
t[n_, m_] := Binomial[m + 1, n - m]; Table[Table[t[n, m], {m, Floor[(n + 1)/2], n}], {n, 0, 15}]; Flatten[%] -
PARI
T(m,n)=binomial(n+1,m-n) \\ Charles R Greathouse IV, May 19 2013
Comments