A054106 Alternating sums of vertically aligned numbers in Pascal's triangle: T(n,k) = C(n,k) - C(n-2,k-1) + C(n-4,k-2) - ... +- C(n-2[n/2],m).

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 5, 3, 1, 1, 4, 8, 8, 4, 1, 1, 5, 12, 15, 12, 5, 1, 1, 6, 17, 27, 27, 17, 6, 1, 1, 7, 23, 44, 55, 44, 23, 7, 1, 1, 8, 30, 67, 99, 99, 67, 30, 8, 1, 1, 9, 38, 97, 166, 197, 166, 97, 38, 9, 1, 1, 10, 47, 135, 263, 363, 363

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			Rows: {1}; {1,1}; {1,1,1}; {1,2,2,1}; {1,3,5,3,1} ...
		

Crossrefs

For (nonalternating) vertically aligned sums, see A013580.

Row sums of this array: A007910.

Formula

G.f.: 1/(1-(1+y)*x)/(1+y*x^2). - Vladeta Jovovic, Oct 12 2003