A097807 Riordan array (1/(1+x),1) read by rows.

1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1

Offset: 0

Author

Paul Barry, Aug 25 2004

Keywords

• easy
• sign
• tabl

Comments

Columns have g.f. x^k/(1+x).

Row sums are A059841. Diagonal sums are (-1)^n*A008619 with g.f. 1/((1+x)(1-x^2)).

Inverse of A097806. Equals B^(-1)*A097805, where B is the binomial matrix.

Examples

			Rows begin
1;
-1,1;
1,-1,1;
-1,1,-1,1;
1,-1,1,-1,1;
		

Crossrefs

Cf. A008619, A059841, A097805, A097806.

Programs

Haskell

a097807 n k = a097807_tabl !! n !! k
a097807_row n = a097807_tabl !! n
a097807_tabl = iterate(\xs@(x:_) -> - x : xs) [1]
-- Reinhard Zumkeller, Sep 17 2014

Mathematica

(* The function RiordanArray is defined in A256893. *)
rows = 12;
R = RiordanArray[1/(1 + #)&, #&, rows];
R // Flatten (* Jean-François Alcover, Jul 20 2019 *)

Formula

Triangle array of numbers T(n, k) with T(n, k)=if(n>=k, (-1)^(n-k), 0).

T(n+1,0) = -T(n,0), T(n+1,k+1) = T(n,k) for k = 1..n. - Reinhard Zumkeller, Sep 17 2014