A112475 Riordan array (1/(1+x),x(1+x)/(1-x)).
1, -1, 1, 1, 1, 1, -1, 1, 3, 1, 1, 1, 5, 5, 1, -1, 1, 7, 13, 7, 1, 1, 1, 9, 25, 25, 9, 1, -1, 1, 11, 41, 63, 41, 11, 1, 1, 1, 13, 61, 129, 129, 61, 13, 1, -1, 1, 15, 85, 231, 321, 231, 85, 15, 1, 1, 1, 17, 113, 377, 681, 681, 377, 113, 17, 1
Offset: 0
Examples
Triangle starts: 1; -1, 1; 1, 1, 1; -1, 1, 3, 1; 1, 1, 5, 5, 1; -1, 1, 7, 13, 7, 1; 1, 1, 9, 25, 25, 9, 1; ...
Programs
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Mathematica
T[n_,k_]:=SeriesCoefficient[(x(1+x)/(1-x))^k/(1+x),{x,0,n}]; Table[T[n,k],{n,0,10},{k,0,n}]//Flatten (* Stefano Spezia, May 26 2024 *)
Formula
T(n,k) = Sum{j=0..n-k} C(k-1,j)*C(n-j-1,n-k-j).
Comments