A109978 Inverse binomial transform of number-theoretic triangle A109974.

1, 1, 1, -1, 1, 1, 2, -2, 2, 1, -5, 5, -4, 5, 1, 13, -14, 11, -7, 12, 1, -33, 40, -35, 20, -5, 27, 1, 80, -111, 113, -77, 21, 34, 58, 1, -184, 293, -350, 294, -144, -27, 238, 121, 1, 402, -731, 1021, -1042, 716, -249, -153, 1063, 248, 1, -840, 1726, -2796, 3409, -2982, 1755, -724, 318, 4037, 503, 1

Offset: 1

Author

Paul Barry, Jul 06 2005

Keywords

• easy
• sign
• tabl

Comments

First column is expansion of bracket function A001659.

Examples

			Rows begin
1;
1,1;
-1,1,1;
2,-2,2,1;
-5,5,-4,5,1;
13,-14,11,-7,12,1;
-33,40,-35,20,-5,27,1;
		

Formula

T(n, k)=sum{j=1..n, (-1)^(n-j)C(n-1, j-1)*if(k<=j, sigma(k-1, j-k+1), 0)} [offset (1, 1)]