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Matrix inverse of triangle A055134.
2

%I #8 Apr 14 2017 03:01:08

%S 1,0,1,-1,-2,1,-2,0,-6,1,-3,0,18,-12,1,-4,0,-40,80,-20,1,-5,0,75,-400,

%T 225,-30,1,-6,0,-126,1680,-1890,504,-42,1,-7,0,196,-6272,13230,-6272,

%U 980,-56,1,-8,0,-288,21504,-81648,64512,-16800,1728,-72,1,-9,0,405

%N Matrix inverse of triangle A055134.

%e 1;

%e 0,1;

%e -1,-2,1;

%e -2,0,-6,1;

%e -3,0,18,-12,1;

%e ...

%t rows = 12; row[n_] := Join[CoefficientList[(x+n-1)^n + O[x]^(n+1), x], Table[0, {rows-n-1}]]; M = Inverse[Table[row[n], {n, 0, rows-1}]]; Table[ M[[n+1, k+1]], {n, 0, rows-1}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Apr 14 2017 *)

%Y Cf. A055136.

%K sign,tabl

%O 0,5

%A _Christian G. Bower_, Apr 25 2000