A110509 Riordan array (1, x(1-2x)).

1, 0, 1, 0, -2, 1, 0, 0, -4, 1, 0, 0, 4, -6, 1, 0, 0, 0, 12, -8, 1, 0, 0, 0, -8, 24, -10, 1, 0, 0, 0, 0, -32, 40, -12, 1, 0, 0, 0, 0, 16, -80, 60, -14, 1, 0, 0, 0, 0, 0, 80, -160, 84, -16, 1, 0, 0, 0, 0, 0, -32, 240, -280, 112, -18, 1, 0, 0, 0, 0, 0, 0, -192, 560, -448, 144, -20, 1, 0, 0, 0, 0, 0, 0, 64, -672, 1120, -672, 180, -22, 1

Offset: 0

Author

Paul Barry, Jul 24 2005

Keywords

• easy
• sign
• tabl

Comments

Inverse is Riordan array (1,xc(2x)) [A110510]. Row sums are A107920(n+1). Diagonal sums are (-1)^n*A052947(n).

Examples

			Rows begin
1;
0,  1;
0, -2,  1;
0,  0, -4,  1;
0,  0,  4, -6,  1;
0,  0,  0, 12, -8,   1;
0,  0,  0, -8, 24, -10, 1;
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Programs

Mathematica

T[n_, k_] := (-2)^(n - k)*Binomial[k, n - k]; Table[T[n, k], {n, 0, 49}, {k, 0, n}] // Flatten (* G. C. Greubel, Aug 29 2017 *)

PARI

for(n=0,25, for(k=0,n, print1((-2)^(n-k)*binomial(k, n-k), ", "))) \\ G. C. Greubel, Aug 29 2017

Formula

Number triangle: T(n, k) = (-2)^(n-k)*binomial(k, n-k).

T(n,k) = A109466(n,k)*2^(n-k). - Philippe Deléham, Oct 26 2008