A112477 Riordan array ((1-x+sqrt(1+6*x+x^2))/2, (sqrt(1+6*x+x^2)-x-1)/2).
1, 1, 1, -2, -1, 1, 6, 2, -3, 1, -22, -6, 10, -5, 1, 90, 22, -38, 22, -7, 1, -394, -90, 158, -98, 38, -9, 1, 1806, 394, -698, 450, -194, 58, -11, 1, -8558, -1806, 3218, -2126, 978, -334, 82, -13, 1, 41586, 8558, -15310, 10286, -4942, 1838, -526, 110, -15, 1, -206098, -41586, 74614, -50746, 25150, -9922, 3142, -778, 142, -17, 1
Offset: 0
Examples
Triangle starts:
1;
1, 1;
-2, -1, 1;
6, 2, -3, 1;
-22, -6, 10, -5, 1;
90, 22, -38, 22, -7, 1;
...
Programs
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Mathematica
T[n_,k_]:=SeriesCoefficient[(1-x+Sqrt[1+6x+x^2])((Sqrt[1+6x+x^2]-x-1)/2)^k/2,{x,0,n}]; Table[T[n,k],{n,0,9},{k,0,n}]//Flatten (* Stefano Spezia, May 26 2024 *)
Comments