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A110517 Riordan array (1,x(1-3x)).

%I A110517 #13 Oct 26 2017 15:54:21
%S A110517 1,0,1,0,-3,1,0,0,-6,1,0,0,9,-9,1,0,0,0,27,-12,1,0,0,0,-27,54,-15,1,0,
%T A110517 0,0,0,-108,90,-18,1,0,0,0,0,81,-270,135,-21,1,0,0,0,0,0,405,-540,189,
%U A110517 -24,1,0,0,0,0,0,-243,1215,-945,252,-27,1,0,0,0,0,0,0,-1458,2835,-1512,324,-30,1,0,0,0,0,0,0,729,-5103,5670,-2268,405
%N A110517 Riordan array (1,x(1-3x)).
%C A110517 Inverse is Riordan array (1,xc(3x)) [A110518]. Row sums are A106852. Diagonal sums are A106855.
%C A110517 Modulo 2, this sequence becomes A106344. - _Philippe Deléham_, Dec 19 2008
%H A110517 G. C. Greubel, <a href="/A110517/b110517.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A110517 Number triangle: T(n, k) = (-3)^(n-k)*binomial(k, n-k).
%F A110517 T(n,k) = A109466(n,k)*3^(n-k). - _Philippe Deléham_, Oct 26 2008
%e A110517 Rows begin
%e A110517 1;
%e A110517 0, 1;
%e A110517 0, -3, 1;
%e A110517 0, 0, -6, 1;
%e A110517 0, 0, 9, -9, 1;
%e A110517 0, 0, 0, 27, -12, 1;
%e A110517 0, 0, 0, -27, 54, -15, 1;
%t A110517 T[n_, k_] := (-3)^(n - k)*Binomial[k, n - k]; Table[T[n, k], {n, 0, 20}, {k, 0, n}] // Flatten (* _G. C. Greubel_, Aug 29 2017 *)
%o A110517 (PARI) for(n=0,20, for(k=0,n, print1((-3)^(n-k)*binomial(k, n-k), ", "))) \\ _G. C. Greubel_, Aug 29 2017
%K A110517 easy,sign,tabl
%O A110517 0,5
%A A110517 _Paul Barry_, Jul 24 2005