%I #24 Apr 19 2019 11:04:56
%S 1,1,1,-1,-2,0,1,1,3,3,0,-3,-1,1,-1,-4,-7,-7,-2,4,6,3,-3,-2,1,1,5,12,
%T 19,21,15,2,-11,-15,-10,-1,7,7,-2,-3,1,-1,-6,-18,-37,-58,-73,-73,-53,
%U -19,17,41,43,25,3,-13,-19,-11,4,11,0,-4,1
%N Irregular triangle formed by coefficients of the polynomials p(k,x) = (x^k - Sum_{j=0..k-1} x^j )*p(k - 1, x), with p(0,x)=1, p(1,x)=x+1, read by rows.
%H G. C. Greubel, <a href="/A123226/b123226.txt">Rows n=0..30 of triangle, flattened</a>
%F Equals coefficients of the polynomials p(k, x) = - ((1 - 2*x^k + x^(k+1))/(1-x))*p(k-1, x), with p(0, x) = 1, p(1, x) = x+1. - _G. C. Greubel_, Mar 23 2019
%e Irregular triangle of coefficients begins as:
%e 1;
%e 1, 1;
%e -1, -2, 0, 1;
%e 1, 3, 3, 0, -3, -1, 1;
%e -1, -4, -7, -7, -2, 4, 6, 3, -3, -2, 1; ...
%t p[0, x] = 1; p[1, x] = x + 1;
%t p[k_, x_]:= p[k, x] = (x^k - Sum[x^m, {m, 0, k-1}])*p[k-1, x];
%t Table[CoefficientList[p[n, x], x], {n, 0, 10}]//Flatten
%Y Cf. A008302.
%K tabf,sign,less
%O 1,5
%A _Roger L. Bagula_, Oct 05 2006