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A155124 Coefficient triangle of polynomial: p(x,m)= -(m - 1) + 2*Sum[x^k, {k, 1, m}]. 1
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, 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, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

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

LINKS

Table of n, a(n) for n=0..65.

FORMULA

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

EXAMPLE

{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, 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, 2, 2}

MATHEMATICA

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

Table[ExpandAll[ -(m - 1) + 2*Sum[n^k, {k, 1, m}]], {m, 1, 10}]'

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

Flatten[%]

CROSSREFS

Sequence in context: A030547 A254690 A156642 * A138033 A283876 A067754

Adjacent sequences:  A155121 A155122 A155123 * A155125 A155126 A155127

KEYWORD

uned,sign

AUTHOR

Roger L. Bagula, Jan 20 2009

STATUS

approved

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Last modified October 18 16:22 EDT 2017. Contains 293524 sequences.