A097807 - OEIS

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

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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;

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: A376149 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