A124756 Inverse binomial sum of compositions in standard order.

0, 1, 2, 0, 3, 1, -1, 0, 4, 2, 0, 1, -2, -2, 1, 0, 5, 3, 1, 2, -1, -1, 2, 1, -3, -4, -1, -3, 2, 3, -1, 0, 6, 4, 2, 3, 0, 0, 3, 2, -2, -3, 0, -2, 3, 4, 0, 1, -4, -6, -3, -6, 0, 0, -4, -4, 3, 6, 2, 6, -2, -4, 1, 0, 7, 5, 3, 4, 1, 1, 4, 3, -1, -2, 1, -1, 4, 5, 1, 2, -3, -5, -2, -5, 1, 1, -3, -3, 4, 7, 3, 7, -1, -3, 2, 1, -5, -8, -5, -9, -2

Offset: 0

Author

Franklin T. Adams-Watters, Nov 06 2006

Keywords

• easy
• sign
• tabf

Comments

The standard order of compositions is given by A066099.

This is the final term of the inverse binomial transform of the composition.

Examples

			Composition number 11 is 2,1,1; 1*2-2*1+1*1 = 1, so a(11) = 1.
The table starts:
0
1
2 0
3 1 -1 0
		

Crossrefs

Cf. A066099, A124754, A124755, A011782 (row lengths), A001477 (row sums).

Formula

For a composition b(1),...,b(k), a(n) = Sum_{i=1}^k (-1)^{i-1} C(k-1,i-1) b(i).