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A100218 Riordan array ((1-2x)/(1-x), (1-x)). 9

%I

%S 1,-1,1,-1,-2,1,-1,0,-3,1,-1,0,2,-4,1,-1,0,0,5,-5,1,-1,0,0,-2,9,-6,1,

%T -1,0,0,0,-7,14,-7,1,-1,0,0,0,2,-16,20,-8,1,-1,0,0,0,0,9,-30,27,-9,1,

%U -1,0,0,0,0,-2,25,-50,35,-10,1,-1,0,0,0,0,0,-11,55,-77,44,-11,1,-1,0,0,0,0,0,2,-36,105,-112,54

%N Riordan array ((1-2x)/(1-x), (1-x)).

%H G. C. Greubel, <a href="/A100218/b100218.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%F Number triangle T(n, k) = (-1)^(n-k)(binomial(k, n-k) + binomial(k-1, n-k-1)). - _Paul Barry_, Nov 09 2004

%F T(n,k) = T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k-1) + T(n-3,k-1), T(0,0)=1, T(1,0)=-1, T(1,1)=1, T(n,k)=0 if k < 0 or if k > n. - _Philippe Deléham_, Jan 09 2014

%e Rows begin {1}, {-1,1}, {-1,-2,1}, {-1,0,-3,1}, {-1,0,2,-4,1},...

%t T[0, 0] := 1; T[1, 1] := 1; T[1, 0] := -1; T[n_, k_] := T[n, k] = If[k < 0 || k > n, 0, T[n - 1, k] + T[n - 1, k - 1] - 2*T[n - 2, k - 1] + T[n - 3, k - 1]]; Table[T[n, k], {n, 0, 49}, {k, 0, n}] // Flatten (* _G. C. Greubel_, Mar 13 2017 *)

%Y Row sums are A100219. Matrix inverse of A100100.

%Y Apart from signs, same as A098599. Very similar to triangle A111125.

%K easy,sign,tabl

%O 0,5

%A _Paul Barry_, Nov 08 2004

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Last modified July 19 09:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)