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Search: id:A137277
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| A137277 |
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False Boubaker polynomials as a triangular sequence of coefficients: alike for the first four rows then different. |
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+0
2
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| 1, 0, 1, 2, 0, 1, 0, 1, 0, 1, -6, 0, 0, 0, 1, 0, -6, 0, -1, 0, 1, 20, 0, -5, 0, -2, 0, 1, 0, 25, 0, -3, 0, -3, 0, 1, -70, 0, 28, 0, 0, 0, -4, 0, 1, 0, -98, 0, 28, 0, 4, 0, -5, 0, 1, 252, 0, -126, 0, 24, 0, 9, 0, -6, 0, 1
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row sums grow slowly and don't repeat as they do in the Boubaker polynomials:
{1, 1, 3, 2, -5, -6, 14, 20, -45, -70, 154}
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REFERENCES
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http://planetmath.org/encyclopedia/BoubakerPolynomials.html
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FORMULA
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B(x,n)=If[n > 0, Sum[(-1)^p*Binomial[n, p]*(n - 4*p)*x^(n - 2*p)/n, {p, 0, Floor[n/2]}], 1]
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EXAMPLE
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{1},
{0, 1},
{2, 0, 1},
{0, 1, 0, 1},
{-6, 0, 0, 0, 1},
{0, -6, 0, -1, 0, 1},
{20, 0, -5, 0, -2, 0, 1},
{0, 25, 0, -3,0, -3, 0, 1},
{-70, 0, 28, 0, 0, 0, -4, 0, 1},
{0, -98, 0, 28, 0,4, 0, -5, 0, 1},
{252, 0, -126, 0, 24, 0, 9, 0, -6, 0, 1}
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MATHEMATICA
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B[x_, n_] = If[n > 0, Sum[(-1)^p*Binomial[n, p]*(n - 4*p)*x^(n - 2*p)/n, {p, 0, Floor[n/2]}], 1]; a = Table[CoefficientList[B[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Cf. A138034.
Sequence in context: A127523 A116927 A140581 this_sequence A039975 A016253 A117188
Adjacent sequences: A137274 A137275 A137276 this_sequence A137278 A137279 A137280
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 13 2008
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