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A110517 Riordan array (1,x(1-3x)). 6

%I #13 Oct 26 2017 15:54:21

%S 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 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 -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 Riordan array (1,x(1-3x)).

%C Inverse is Riordan array (1,xc(3x)) [A110518]. Row sums are A106852. Diagonal sums are A106855.

%C Modulo 2, this sequence becomes A106344. - _Philippe Deléham_, Dec 19 2008

%H G. C. Greubel, <a href="/A110517/b110517.txt">Table of n, a(n) for the first 50 rows, flattened</a>

%F Number triangle: T(n, k) = (-3)^(n-k)*binomial(k, n-k).

%F T(n,k) = A109466(n,k)*3^(n-k). - _Philippe Deléham_, Oct 26 2008

%e Rows begin

%e 1;

%e 0, 1;

%e 0, -3, 1;

%e 0, 0, -6, 1;

%e 0, 0, 9, -9, 1;

%e 0, 0, 0, 27, -12, 1;

%e 0, 0, 0, -27, 54, -15, 1;

%t 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 (PARI) for(n=0,20, for(k=0,n, print1((-3)^(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

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)