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%I #6 Jan 03 2022 20:36:41
%S 0,1,-2,1,1,0,-3,2,1,0,0,-4,3,1,0,0,0,-5,4,1,0,0,0,0,-6,5,1,0,0,0,0,0,
%T -7,6,1,0,0,0,0,0,0,-8,7,1,0,0,0,0,0,0,0,-9,8,1,0,0,0,0,0,0,0,0,-10,9,
%U 1,0,0,0,0,0,0,0,0,0,-11,10
%N Triangle of coefficients of 1 - (n+1)*x^n + n*x^(n+1), read by rows.
%H G. C. Greubel, <a href="/A156578/b156578.txt">Rows n = 0..50 if the irregular triangle, flattened</a>
%F T(n, k) = [x^k]( (1-x)^2 * Sum_{j=0..n-1} (j+1)*x^j ).
%F T(n, k) = [k=0] - (n+1)*[k=n] + n*[k=n+1] for n > 0, with T(0, 0) = 0. - _G. C. Greubel_, Jan 03 2022
%e Irregular triangle begins as:
%e 0;
%e 1, -2, 1;
%e 1, 0, -3, 2;
%e 1, 0, 0, -4, 3;
%e 1, 0, 0, 0, -5, 4;
%e 1, 0, 0, 0, 0, -6, 5;
%e 1, 0, 0, 0, 0, 0, -7, 6;
%e 1, 0, 0, 0, 0, 0, 0, -8, 7;
%e 1, 0, 0, 0, 0, 0, 0, 0, -9, 8;
%e 1, 0, 0, 0, 0, 0, 0, 0, 0, -10, 9;
%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 10;
%e ...
%t T[n_]:= If[n==0, 0, CoefficientList[1 -(n+1)*x^n +n*x^(n+1), x]];
%t Table[T[n], {n,0,15}]//Flatten (* modified by _G. C. Greubel_, Jan 03 2022 *)
%o (Sage) [0]+flatten([[( 1 -(n+1)*x^n +n*x^(n+1) ).series(x, n+2).list()[k] for k in (0..n+1)] for n in (1..12)]) # _G. C. Greubel_, Jan 03 2022
%K sign,tabf,less
%O 0,3
%A _Roger L. Bagula_, Feb 10 2009
%E Edited by _G. C. Greubel_, Jan 03 2022
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