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A168290
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Coefficients of the expansion of:w=5;p(t,x)=(1 - w)Exp[t*(1 + x)] + w(1 - x)*(Exp[t])/(1 - x*Exp[t*(1 - x)])
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0
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1, 1, 1, 1, 7, 1, 1, 23, 23, 1, 1, 59, 141, 59, 1, 1, 135, 615, 615, 135, 1, 1, 291, 2305, 4335, 2305, 291, 1, 1, 607, 7971, 25415, 25415, 7971, 607, 1, 1, 1243, 26293, 133771, 224365, 133771, 26293, 1243, 1, 1, 2519, 84191, 656039, 1722251, 1722251, 656039
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OFFSET
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0,5
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COMMENTS
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A umbral calculus expansion made from a Bezier extrapolation of the Pascal and A046802.
Row sums are:
{1, 2, 9, 48, 261, 1502, 9529, 67988, 546981, 4930002, 49316409,...}
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LINKS
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Table of n, a(n) for n=0..51.
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FORMULA
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w=5;p(t,x)=(1 - w)Exp[t*(1 + x)] + w(1 - x)*(Exp[t])/(1 - x*Exp[t*(1 - x)])
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EXAMPLE
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{1},
{1, 1},
{1, 7, 1},
{1, 23, 23, 1},
{1, 59, 141, 59, 1},
{1, 135, 615, 615, 135, 1},
{1, 291, 2305, 4335, 2305, 291, 1},
{1, 607, 7971, 25415, 25415, 7971, 607, 1},
{1, 1243, 26293, 133771, 224365, 133771, 26293, 1243, 1},
{1, 2519, 84191, 656039, 1722251, 1722251, 656039, 84191, 2519, 1},
{1, 5075, 264345, 3062055, 12001605, 18650247, 12001605, 3062055, 264345, 5075, 1}
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MATHEMATICA
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w = 5; p[t_] = (1 - w)Exp[t*(1 + x)] + w(1 - x)*(Exp[t])/(1 - x*Exp[t*(1 - x)])
a = Table[CoefficientList[FullSimplify[ExpandAll[n!*SeriesCoefficient[Series[p[ t], {t, 0, 30}], n]]], x], {n, 0, 10}];
Flatten[a]
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CROSSREFS
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A046802
Sequence in context: A046739 A056752 A053714 * A218695 A179837 A168517
Adjacent sequences: A168287 A168288 A168289 * A168291 A168292 A168293
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula, Nov 22 2009
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STATUS
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approved
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