A110168 Riordan array ((1-x^2)/(1+3x+x^2),x/(1+3x+x^2)).

1, -3, 1, 7, -6, 1, -18, 24, -9, 1, 47, -84, 50, -12, 1, -123, 275, -225, 85, -15, 1, 322, -864, 900, -468, 129, -18, 1, -843, 2639, -3339, 2219, -840, 182, -21, 1, 2207, -7896, 11756, -9528, 4610, -1368, 244, -24, 1, -5778, 23256, -39825, 38121, -22518, 8532, -2079, 315, -27, 1, 15127, -67650, 130975

Offset: 0

Author

Paul Barry, Jul 14 2005

Keywords

• easy
• sign
• tabl

Comments

Inverse of A110165. Row sums are 1,-2,2,-2,... with g.f. (1-x)/(1+x). Diagonal sums are (-1)^n*A080923. Product of A110162 and inverse binomial transform (1/(1+x),x/(1+x)).

Examples

			Rows begin
1;
-3,1;
7,-6,1;
-18,24,-9,1;
47,-84,50,-12,1;
-123,275,-225,85,-15,1;
		

Formula

T(n,k) = T(n-1,k-1) - 3*T(n-1,k) - T(n-2,k), T(0,0) = T(1,1) = T(2,2) = 1, T(1,0) = -3, T(2,0) = 7, T(2,1) = -6, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 22 2014