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A097807 Riordan array (1/(1+x),1) read by rows. 11

%I

%S 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,

%T -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,

%U -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

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

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

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

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

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

%F T(n+1,0) = -T(n,0), T(n+1,k+1) = T(n,k) for k = 1..n. - _Reinhard Zumkeller_, Sep 17 2014

%e Rows begin

%e 1;

%e -1,1;

%e 1,-1,1;

%e -1,1,-1,1;

%e 1,-1,1,-1,1;

%t (* The function RiordanArray is defined in A256893. *)

%t rows = 12;

%t R = RiordanArray[1/(1 + #)&, #&, rows];

%t R // Flatten (* _Jean-Fran├žois Alcover_, Jul 20 2019 *)

%o (Haskell)

%o a097807 n k = a097807_tabl !! n !! k

%o a097807_row n = a097807_tabl !! n

%o a097807_tabl = iterate(\xs@(x:_) -> - x : xs) [1]

%o -- _Reinhard Zumkeller_, Sep 17 2014

%Y Cf. A008619, A059841, A097805, A097806.

%K easy,sign,tabl

%O 0,1

%A _Paul Barry_, Aug 25 2004

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)