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A155124 Coefficient triangle of polynomial: p(x,m)= -(m - 1) + 2*Sum[x^k, {k, 1, m}]. 1

%I

%S 1,0,2,-1,2,2,-2,2,2,2,-3,2,2,2,2,-4,2,2,2,2,2,-5,2,2,2,2,2,2,-6,2,2,

%T 2,2,2,2,2,-7,2,2,2,2,2,2,2,2,-8,2,2,2,2,2,2,2,2,2,-9,2,2,2,2,2,2,2,2,

%U 2,2

%N Coefficient triangle of polynomial: p(x,m)= -(m - 1) + 2*Sum[x^k, {k, 1, m}].

%C Row sums are :n;{1,2,3,4,5,6,7,8,9,10,...}

%C These polynomials in n are column functions for general Pascal-Sierpinski triangles.

%F p(x,m)= -(m - 1) + 2*Sum[x^k, {k, 1, m}]; t(m,n)=coefficients(p(x,m))

%e {1},

%e {0, 2},

%e {-1, 2, 2},

%e {-2, 2, 2, 2},

%e {-3, 2, 2, 2, 2},

%e {-4, 2, 2, 2, 2, 2},

%e {-5, 2, 2, 2, 2, 2, 2},

%e {-6, 2, 2, 2, 2, 2, 2, 2},

%e {-7, 2, 2, 2, 2, 2, 2, 2, 2},

%e {-8, 2, 2, 2, 2, 2, 2, 2, 2, 2},

%e {-9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2}

%t Clear[f, n, m]; f[n_, m_] = -(m - 1) + 2*Sum[n^k, {k, 1, m}];

%t Table[ExpandAll[ -(m - 1) + 2*Sum[n^k, {k, 1, m}]], {m, 1, 10}]'

%t Table[CoefficientList[ExpandAll[ -(m - 1) + 2*Sum[n^ k, {k, 1, m}]], n], {m, 0, 10}];

%t Flatten[%]

%K uned,sign

%O 0,3

%A _Roger L. Bagula_, Jan 20 2009

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Last modified February 28 09:13 EST 2021. Contains 341695 sequences. (Running on oeis4.)