A128414 Riordan array ((1-2x)/(1+2x),x/(1+2x)^2).

1, -4, 1, 8, -8, 1, -16, 36, -12, 1, 32, -128, 80, -16, 1, -64, 400, -400, 140, -20, 1, 128, -1152, 1680, -896, 216, -24, 1, -256, 3136, -6272, 4704, -1680, 308, -28, 1, 512, -8192, 21504, -21504, 10560, -2816

Offset: 0

Author

Paul Barry, Mar 02 2007

Keywords

• easy
• sign
• tabl

Comments

Inverse is A128417. Row sums are A128415. Diagonal sums are A128416.

Examples

			Triangle begins
1;
-4, 1;
8, -8, 1;
-16, 36, -12, 1;
32, -128, 80, -16, 1;
-64, 400, -400, 140, -20, 1;
128, -1152, 1680, -896, 216, -24, 1;
-256, 3136, -6272, 4704, -1680, 308, -28, 1;
512, -8192, 21504, -21504, 10560, -2816, 416, -32, 1;
		

Crossrefs

Cf. A128413.

Formula

T(n,k) = 2^(n-k)*A110162(n,k). - Philippe Deléham, Jan 18 2014

T(n,k) = T(n-1,k-1) - 4*T(n-1,k) - 4*T(n-2,k), T(0,0) = T(1,1) = T(2,2) = 1, T(1,0) = -4, T(2,0) = 8, T(2,1) = -8, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 18 2014