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%I #17 Jul 20 2019 12:33:39
%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-François 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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