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Search: id:A144387
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| A144387 |
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A prime based false Bezier of polynomials: a triangle sequence of coefficients; p(x,n)=Sum[Prime[k + 1]*x^k*(1 - x)^(n - k), {k, 0, n}]. |
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1
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| 2, 2, 1, 2, -1, 4, 2, -3, 5, 3, 2, -5, 8, -2, 8, 2, -7, 13, -10, 10, 5, 2, -9, 20, -23, 20, -5, 12, 2, -11, 29, -43, 43, -25, 17, 7, 2, -13, 40, -72, 86, -68, 42, -10, 16, 2, -15, 53, -112, 158, -154, 110, -52, 26, 13, 2, -17, 68, -165, 270, -312, 264, -162, 78, -13, 18
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Row sums are the primes:
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31}.
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FORMULA
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p(x,n)=Sum[Prime[k + 1]*x^k*(1 - x)^(n - k), {k, 0, n}]; t(n,m)=coefficients(p(x,n)).
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EXAMPLE
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{2},
{2, 1},
{2, -1, 4},
{2, -3, 5, 3},
{2, -5, 8, -2, 8},
{2, -7, 13, -10, 10, 5},
{2, -9, 20, -23, 20, -5, 12},
{2, -11, 29, -43, 43, -25, 17, 7},
{2, -13, 40, -72, 86, -68, 42, -10, 16},
{2, -15, 53, -112,158, -154, 110, -52, 26, 13},
{2, -17, 68, -165, 270, -312, 264, -162, 78, -13, 18}
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MATHEMATICA
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Clear[p, x, n, m]; p[x_, n_] = Sum[Prime[k + 1]*x^k*(1 - x)^(n - k), {k, 0, n}]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A105153 A000924 A109909 this_sequence A030768 A051480 A071572
Adjacent sequences: A144384 A144385 A144386 this_sequence A144388 A144389 A144390
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 01 2008
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