cp's OEIS Frontend

A140575 Triangle read by rows: the coefficient of [x^k] of the polynomial 1-(x-1)^n in row n and column k, 0<=k

%I A140575 #11 Aug 12 2015 14:55:59
%S A140575 0,2,-1,0,2,-1,2,-3,3,-1,0,4,-6,4,-1,2,-5,10,-10,5,-1,0,6,-15,20,-15,
%T A140575 6,-1,2,-7,21,-35,35,-21,7,-1,0,8,-28,56,-70,56,-28,8,-1,2,-9,36,-84,
%U A140575 126,-126,84,-36,9,-1,0,10,-45,120,-210,252,-210,120,-45,10,-1
%N A140575 Triangle read by rows: the coefficient of [x^k] of the polynomial 1-(x-1)^n in row n and column k, 0<=k<n.
%C A140575 Row sums are: 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...;
%C A140575 This is the Pascal Triangle A007318 with alternating signs and the leading column of 1's replaced alternatingly by 0 and 2. - _R. J. Mathar_, Sep 09 2013
%C A140575 With T(0,0) = 1, this is (2, -2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (-1, 2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, May 24 2015
%C A140575 G.f.: (1+2*x-x^2-2*x*y+x^2*y)/((-1+x)*(-x+x*y-1)) -1 - _R. J. Mathar_, Aug 12 2015
%F A140575 T(n,k) = T(n-1,k-1) + T(n-2,k) - T(n-2,k-1), T(0,0) = 0, T(1,0) = 2, T(1,1) = -1, T(n,k) = 0 if k>n or if k<0. - _Philippe Deléham_, May 24 2015
%e A140575 0;
%e A140575 2, -1;
%e A140575 0, 2, -1;
%e A140575 2, -3, 3, -1;
%e A140575 0, 4, -6, 4, -1;
%e A140575 2, -5, 10, -10, 5, -1;
%e A140575 0, 6, -15, 20, -15, 6, -1;
%e A140575 2, -7, 21, -35, 35, -21, 7, -1;
%e A140575 0, 8, -28,56, -70, 56, -28, 8, -1;
%e A140575 2, -9, 36, -84, 126, -126, 84, -36, 9, -1;
%e A140575 0, 10, -45, 120, -210, 252, -210, 120, -45, 10, -1;
%t A140575 Clear[p] p[x, 0] = 1; p[x, 1] = x - 1; p[x_, n_] := x^n*(1/x^n - (1 - 1/x)^n); a = Table[ExpandAll[p[x, n]], {n, 0, 10}]; b = Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}]; Flatten[b]
%Y A140575 Cf. A091917.
%K A140575 tabl,easy,sign
%O A140575 0,2
%A A140575 _Roger L. Bagula_ and _Gary W. Adamson_, Jul 05 2008