A119331 Number triangle T(n,k)=sum{i=0..n, (-1)^(n-i)*C(n,i)*sum{j=0..i-k, C(k,2j)*C(i-k,2j)*2^j}}.

1, 0, 1, 0, -1, 1, 0, 1, -2, 1, 0, -1, 5, -3, 1, 0, 1, -8, 12, -4, 1, 0, -1, 11, -28, 22, -5, 1, 0, 1, -14, 51, -68, 35, -6, 1, 0, -1, 17, -81, 159, -135, 51, -7, 1, 0, 1, -20, 118, -312, 390, -236, 70, -8, 1, 0, -1, 23, -162, 544, -926, 816, -378, 92, -9, 1

Offset: 0

Author

Paul Barry, May 14 2006

Keywords

• easy
• sign
• tabl

Comments

Row sums are A119332. Multiply by Pascal's triangle A007318 to get A119329.

Examples

			Triangle begins
1,
0, 1,
0, -1, 1,
0, 1, -2, 1,
0, -1, 5, -3, 1,
0, 1, -8, 12, -4, 1,
0, -1, 11, -28, 22, -5, 1,
0, 1, -14, 51, -68, 35, -6, 1,
0, -1, 17, -81, 159, -135, 51, -7, 1,
0, 1, -20, 118, -312, 390, -236, 70, -8, 1,
0, -1, 23, -162, 544, -926, 816, -378, 92, -9, 1
		

Formula

Column k has g.f. (x/(1+x))^k*sum{j=0..k, C(k,2j)*2^j*x^(2j)}