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%I #9 Jul 03 2014 22:19:30
%S 1,-1,1,0,-3,1,0,4,-5,1,0,-4,12,-7,1,0,4,-20,24,-9,1,0,-4,28,-56,40,
%T -11,1,0,4,-36,104,-120,60,-13,1,0,-4,44,-168,280,-220,84,-15,1,0,4,
%U -52,248,-552,620,-364,112,-17,1,0,-4,60,-344,968,-1452,1204,-560,144,-19,1
%N Riordan array (1-x, x(1-x)/(1+x)).
%C Inverse of A186826. Row sums are A176742. Diagonal sums are the alternating sign tribonacci numbers (-1)^n*A000213(n).
%D C.-P. Chou, H. A. Witek, ZZDecomposer: A Graphical Toolkit for Analyzing the Zhang-Zhang Polynomials of Benzenoid Structures, MATCH: Communications in Mathematical and in Computer Chemistry. 71 (2014) 741-764. See Eq. (13). - _N. J. A. Sloane_, Jul 03 2014
%F Triangle T(n,k)=(-1)^(n-k)*sum{j=0..k+1, binomial(k+1,j)*binomial(n-j-1,n-k-j)}.
%F T(n,k)=T(n-1,k-1)-T(n-1,k)-T(n-2,k-1), T(0,0)=1, T(1,0)=-1, T(1,1)=1, T(2,0)=0, T(2,1)=-3, T(2,2)=1, T(n,k)=0 if k<0 or if k>n. - _Philippe Deléham_, Jan 12 2014
%e Triangle begins
%e 1,
%e -1, 1,
%e 0, -3, 1,
%e 0, 4, -5, 1,
%e 0, -4, 12, -7, 1,
%e 0, 4, -20, 24, -9, 1,
%e 0, -4, 28, -56, 40, -11, 1,
%e 0, 4, -36, 104, -120, 60, -13, 1,
%e 0, -4, 44, -168, 280, -220, 84, -15, 1,
%e 0, 4, -52, 248, -552, 620, -364, 112, -17, 1,
%e 0, -4, 60, -344, 968, -1452, 1204, -560, 144, -19, 1
%K sign,easy,tabl
%O 0,5
%A _Paul Barry_, Feb 27 2011
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