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

0,1

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.

Links

Table of n, a(n) for n=0..80.

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A008619, A059841, A097805, A097806.

Sequence in context: A244513 A020985 A034947 * A014077 A174351 A339265

Adjacent sequences: A097804 A097805 A097806 * A097808 A097809 A097810

Keyword

easy,sign,tabl

Author

Paul Barry, Aug 25 2004

Status

approved