A110517 Riordan array (1,x(1-3x)).

1, 0, 1, 0, -3, 1, 0, 0, -6, 1, 0, 0, 9, -9, 1, 0, 0, 0, 27, -12, 1, 0, 0, 0, -27, 54, -15, 1, 0, 0, 0, 0, -108, 90, -18, 1, 0, 0, 0, 0, 81, -270, 135, -21, 1, 0, 0, 0, 0, 0, 405, -540, 189, -24, 1, 0, 0, 0, 0, 0, -243, 1215, -945, 252, -27, 1, 0, 0, 0, 0, 0, 0, -1458, 2835, -1512, 324, -30, 1, 0, 0, 0, 0, 0, 0, 729, -5103, 5670, -2268, 405

Offset: 0

Author

Paul Barry, Jul 24 2005

Keywords

• easy
• sign
• tabl

Comments

Inverse is Riordan array (1,xc(3x)) [A110518]. Row sums are A106852. Diagonal sums are A106855.

Modulo 2, this sequence becomes A106344. - Philippe Deléham, Dec 19 2008

Examples

			Rows begin
1;
0, 1;
0, -3, 1;
0, 0, -6, 1;
0, 0, 9, -9, 1;
0, 0, 0, 27, -12, 1;
0, 0, 0, -27, 54, -15, 1;
		

Links

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

Programs

Mathematica

T[n_, k_] := (-3)^(n - k)*Binomial[k, n - k]; Table[T[n, k], {n, 0, 20}, {k, 0, n}] // Flatten (* G. C. Greubel, Aug 29 2017 *)

PARI

for(n=0,20, for(k=0,n, print1((-3)^(n-k)*binomial(k, n-k), ", "))) \\ G. C. Greubel, Aug 29 2017

Formula

Number triangle: T(n, k) = (-3)^(n-k)*binomial(k, n-k).

T(n,k) = A109466(n,k)*3^(n-k). - Philippe Deléham, Oct 26 2008