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Triangle: a(n,k) = A055135(n,k)/C(n,k).
2

%I #9 Apr 14 2017 03:01:15

%S 1,0,1,-1,-1,1,-2,0,-2,1,-3,0,3,-3,1,-4,0,-4,8,-4,1,-5,0,5,-20,15,-5,

%T 1,-6,0,-6,48,-54,24,-6,1,-7,0,7,-112,189,-112,35,-7,1,-8,0,-8,256,

%U -648,512,-200,48,-8,1,-9,0,9,-576,2187,-2304,1125,-324,63,-9,1,-10,0

%N Triangle: a(n,k) = A055135(n,k)/C(n,k).

%F n, k>1: a(n, k) = (-1)^(n+k)*(n-1)*(k-1)^(n-k-1).

%e 1;

%e 0,1;

%e -1,-1,1;

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

%e -3,0,3,-3,1; ...

%t a[n_, k_] := (-1)^(n+k)*(n-1)*(k-1)^(n-k-1); a[1, 1] = a[2, 1] = 1; Table[ a[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Apr 14 2017 *)

%K sign,tabl

%O 0,7

%A _Christian G. Bower_, Apr 25 2000