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Search: id:A139167
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| A139167 |
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A triangular sequence of coefficients from an Hibert polynomial with Fibonacci indexing coefficients from the Fibonacci number a000045: p(x,n)=sum(A000045(i)*Binomial[x.n-i],{i,0,n}]. |
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+0
1
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| 1, 1, 1, 4, 1, 1, 18, 11, 0, 1, 120, 50, 23, -2, 1, 960, 494, 65, 45, -5, 1, 9360, 4344, 1354, -15, 85, -9, 1, 105840, 51876, 10444, 3409, -350, 154, -14, 1, 1370880, 653232, 172444, 13300, 8729, -1232, 266, -20, 1, 19958400, 9654480, 2194380, 483272, -13923, 22449, -3150, 438, -27, 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 are:
{0, 1, 2, 6, 30, 192, 1560, 15120, 171360, 2217600, 32296320}.
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REFERENCES
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Brendan Hassett, Introduction to algebraic Geometry,Cambridge University Press. New York,2007, page 229
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FORMULA
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p(x,n)=sum(A000045(i)*Binomial[x.n-i],{i,0,n}]; out_n,m=Coefficients((n-1)!*p(x,n).
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EXAMPLE
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{0},
{1},
{1, 1},
{4, 1, 1},
{18, 11, 0, 1},
{120, 50, 23, -2, 1},
{960, 494, 65, 45, -5, 1},
{9360, 4344, 1354, -15,85, -9, 1},
{105840, 51876, 10444, 3409, -350, 154, -14, 1},
{1370880, 653232, 172444, 13300, 8729, -1232, 266, -20, 1},
{19958400, 9654480, 2194380, 483272, -13923, 22449, -3150, 438, -27, 1}
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MATHEMATICA
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Clear[a, p, x] a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2]; p[x, 0] = a[0]; p[x_, n_] := p[x, n] = Sum[a[i]*Binomial[x, n - i], {i, 0, n}]; Table[If[n > 0, ExpandAll[(n - 1)!*p[x, n]], 0], {n, 0, 10}]; a = Table[CoefficientList[If[n > 0, ExpandAll[(n - 1)!*p[x, n]], 0], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[If[n > 0, ExpandAll[(n - 1)!*p[x, n]], 0], x]], {n, 0, 10}]
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CROSSREFS
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Cf. A000045.
Sequence in context: A008304 A118185 A034802 this_sequence A156586 A154283 A015113
Adjacent sequences: A139164 A139165 A139166 this_sequence A139168 A139169 A139170
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KEYWORD
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uned,tabf,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 05 2008
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