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%I #19 Nov 22 2014 03:47:40
%S 1,-2,1,-29,7,1,268,-74,-8,1,4885,-1262,-170,13,1,-82838,21823,2800,
%T -257,-14,1,-2097065,548161,72055,-6197,-419,19,1,51727192,-13551428,
%U -1770128,155398,9976,-548,-20,1,1696812649,-444145484,-58168484,5067886,333166,-17180,-776,25,1
%N Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} x^k = Sum_{k=0..n} A_k*(x-3*(-1)^k)^k.
%C Consider the transformation 1 + x + x^2 + x^3 + ... + x^n = A_0*(x-3)^0 + A_1*(x+3)^1 + A_2*(x-3)^2 + A_3*(x+3)^3 + ... + A_n*(x-3*(-1)^n)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0.
%e Triangle starts:
%e 1;
%e -2, 1;
%e -29, 7, 1;
%e 268, -74, -8, 1;
%e 4885, -1262, -170, 13, 1;
%e -82838, 21823, 2800, -257, -14, 1;
%e -2097065, 548161, 72055, -6197, -419, 19, 1;
%e 51727192, -13551428, -1770128, 155398, 9976, -548, -20, 1;
%e 1696812649, -444145484, -58168484, 5067886, 333166, -17180, -776, 25, 1;
%e ...
%o (PARI) a(n, j, L)=if(j==n, return(1)); if(j!=n, return(1-sum(i=1, n-j, (-L)^i*(-1)^(i*j)*binomial(i+j, i)*a(n, i+j, L))))
%o for(n=0, 10, for(j=0, n, print1(a(n, j, -3), ", ")))
%Y Cf. A248978, A248976.
%K sign,tabl
%O 0,2
%A _Derek Orr_, Oct 23 2014
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