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Riordan array (1, x(1-2x)).
7

%I #17 Aug 29 2017 22:50:36

%S 1,0,1,0,-2,1,0,0,-4,1,0,0,4,-6,1,0,0,0,12,-8,1,0,0,0,-8,24,-10,1,0,0,

%T 0,0,-32,40,-12,1,0,0,0,0,16,-80,60,-14,1,0,0,0,0,0,80,-160,84,-16,1,

%U 0,0,0,0,0,-32,240,-280,112,-18,1,0,0,0,0,0,0,-192,560,-448,144,-20,1,0,0,0,0,0,0,64,-672,1120,-672,180,-22,1

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

%C Inverse is Riordan array (1,xc(2x)) [A110510]. Row sums are A107920(n+1). Diagonal sums are (-1)^n*A052947(n).

%H G. C. Greubel, <a href="/A110509/b110509.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%F Number triangle: T(n, k) = (-2)^(n-k)*binomial(k, n-k).

%F T(n,k) = A109466(n,k)*2^(n-k). - _Philippe Deléham_, Oct 26 2008

%e Rows begin

%e 1;

%e 0, 1;

%e 0, -2, 1;

%e 0, 0, -4, 1;

%e 0, 0, 4, -6, 1;

%e 0, 0, 0, 12, -8, 1;

%e 0, 0, 0, -8, 24, -10, 1;

%t T[n_, k_] := (-2)^(n - k)*Binomial[k, n - k]; Table[T[n, k], {n, 0, 49}, {k, 0, n}] // Flatten (* _G. C. Greubel_, Aug 29 2017 *)

%o (PARI) for(n=0,25, for(k=0,n, print1((-2)^(n-k)*binomial(k, n-k), ", "))) \\ _G. C. Greubel_, Aug 29 2017

%K easy,sign,tabl

%O 0,5

%A _Paul Barry_, Jul 24 2005