A105847 Inverse binomial transform of number triangle A105632.

1, 0, 1, 1, -1, 1, 0, 3, -2, 1, 2, -3, 6, -3, 1, 0, 9, -10, 10, -4, 1, 5, -9, 26, -22, 15, -5, 1, 0, 29, -42, 59, -40, 21, -6, 1, 14, -29, 108, -121, 115, -65, 28, -7, 1, 0, 99, -174, 308, -276, 202, -98, 36, -8, 1, 42, -99, 450, -620, 734, -546, 329, -140, 45, -9, 1, 0, 351, -726, 1547, -1700, 1540, -980, 506, -192, 55, -10, 1, 132

Offset: 0

Author

Paul Barry, Apr 22 2005

Keywords

• easy
• sign
• tabl

Comments

Product of Riordan array (1/(1+x),x/(1+x)) (inverse binomial matrix) and A105632. Rows sums are A007477.

Examples

			Triangle begins
1;
0,1;
1,-1,1;
0,3,-2,1;
2,-3,6,-3,1;
0,9,-10,10,-4,1;
		

Formula

Column k has g.f. (sum{j=0..k-1, C(k-1, j)C(j)x^(2j)/(1-4x^2)^(j+1/2)}+0^k*(1-sqrt(1-4x^2))/(2x^2))(x/(1+x))^k