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%I #36 Jun 28 2018 17:30:31
%S 1,3,-2,9,-12,4,27,-54,36,-8,81,-216,216,-96,16,243,-810,1080,-720,
%T 240,-32,729,-2916,4860,-4320,2160,-576,64,2187,-10206,20412,-22680,
%U 15120,-6048,1344,-128,6561,-34992,81648,-108864,90720,-48384,16128,-3072,256,19683,-118098,314928,-489888,489888
%N Triangle read by rows of coefficients in expansion of (3-2x)^n, where n is a nonnegative integer.
%C This is a signed version of A038220.
%C Row n gives coefficients in expansion of (3-2x)^n.
%C The numbers in rows of triangles in A302747 and A303941 are along skew diagonals pointing top-left and top-right in center-justified triangle of coefficients in expansions of (3-2x)^n (A303901).
%C This is the lower triangular Riordan matrix (1/(1 - 3*t), -2*t/(1-3*t), hence a convolution matrix.See the g.f.s. - _Wolfdieter Lang_, Jun 28 2018
%D Shara Lalo and Zagros Lalo, Polynomial Expansion Theorems and Number Triangles, Zana Publishing, 2018, ISBN: 978-1-9995914-0-3, pp. 394, 396, 398.
%H Zagros Lalo, <a href="/A303901/a303901_1.pdf">Center-justified Triangle</a>
%H Zagros Lalo, <a href="/A303901/a303901_2.pdf">Skew Diagonals in center-justified Triangle</a>
%F T(0,0) = 1; T(n,k) = 3*T(n-1,k) -2*T(n-1,k-1) for k = 0,1,...,n; T(n,k)=0 for n or k < 0.
%F G.f. of row polynomials: 1 / (1 - 3t + 2t x).G.f. of column k: (-2*x)^k/(1-3*x)^(k+1), for k >= 0.
%e Triangle begins:
%e n \k 0 1 2 3 4 5 6 7 8 9 ...
%e --------------------------------------------------------------------------
%e 0 | 1
%e 1 | 3 -2
%e 2 | 9 -12 4
%e 3 | 27 -54 36 -8
%e 4 | 81 -216 216 -96 16
%e 5 | 243 -810 1080 -720 240 -32
%e 6 | 729 -2916 4860 -4320 2160 -576 64
%e 7 | 2187 -10206 20412 -22680 15120 -6048 1344 -128
%e 8 | 6561 -34992 81648 -108864 90720 -48384 16128 -3072 256
%e 9 | 19683 -118098 314928 -489888 489888 -326592 145152 -41472 6912 -512
%e …
%t For[i = 0, i < 4, i++, Print[CoefficientList[Expand[(3 - 2 x)^i],x]]]
%Y Cf. A013620 (unsigned), A000012 (row sums), A000351 (alternating row sums).
%K tabl,easy,sign
%O 0,2
%A _Zagros Lalo_, May 02 2018
%E Edited - _Wolfdieter Lang_, Jun 28 2018