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 A168290 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)]) 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS 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,...} LINKS FORMULA w=5;p(t,x)=(1 - w)Exp[t*(1 + x)] + w(1 - x)*(Exp[t])/(1 - x*Exp[t*(1 - x)]) EXAMPLE {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} MATHEMATICA 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] CROSSREFS Sequence in context: A046739 A056752 A053714 * A218695 A179837 A168517 Adjacent sequences:  A168287 A168288 A168289 * A168291 A168292 A168293 KEYWORD nonn,uned AUTHOR Roger L. Bagula, Nov 22 2009 STATUS approved

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