A055136 Triangle: a(n,k) = A055135(n,k)/C(n,k).

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, 1, -6, 0, -6, 48, -54, 24, -6, 1, -7, 0, 7, -112, 189, -112, 35, -7, 1, -8, 0, -8, 256, -648, 512, -200, 48, -8, 1, -9, 0, 9, -576, 2187, -2304, 1125, -324, 63, -9, 1, -10, 0

Offset: 0

Author

Christian G. Bower, Apr 25 2000

Keywords

• sign
• tabl

Examples

			1;
0,1;
-1,-1,1;
-2,0,-2,1;
-3,0,3,-3,1; ...
		

Programs

Mathematica

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 *)

Formula

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