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Search: id:A137523
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| A137523 |
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A triangular sequence from an expansion of coefficients of the function: p(x,t)=Exp(x*g*(t))*(1-f(t)^2);f(t)=1/Sqrt[1 - 2*t^2 + t^4];g(t)=t. (based on the Weierstrass functions of Jenkins -Serrin minimal surface). |
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1
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| 0, 0, -4, 0, -12, -72, 0, -24, 0, -360, 0, -40, -2880, 0, -1080, 0, -60, 0, -20160, 0, -2520, 0, -84, -201600, 0, -80640, 0, -5040, 0, -112, 0, -1814400, 0, -241920, 0, -9072, 0, -144, -21772800, 0, -9072000, 0, -604800, 0, -15120, 0, -180
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row sums:
{0, 0, -4, -12, -96, -400, -4020, -22764, -287392, -2065536, -31464900};
Because of the 4th power in generator function nothing shows up until n=3.
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REFERENCES
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Francisco J. Lopez,Francisco Martin,Complete minimal surfaces in R^3,April 11, 2000, web pdf, page 16
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FORMULA
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p(x,t)=Exp(x*g*(t))*(1-f(t)^2);f(t)=1/Sqrt[1 - 2*t^2 + t^4];g(t)=t; p(x,t)=Sum[P(x,n)*t^n/n!,{n,0,Infinity}]; Out_n,m=(n!)*Coefficients(P(x,n).
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EXAMPLE
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{0},
{0},
{-4},
{0, -12},
{-72, 0, -24},
{0, -360,0, -40},
{-2880, 0, -1080, 0, -60},
{0, -20160, 0, -2520, 0, -84},
{-201600, 0, -80640, 0, -5040, 0, -112},
{0, -1814400, 0, -241920, 0, -9072, 0, -144},
{-21772800, 0, -9072000, 0, -604800, 0, -15120, 0, -180}
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MATHEMATICA
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Clear[p, f, g] g[t_] = t; f[t] = 1/Sqrt[1 - 2*t^2 + t^4]; p[t_] = Exp[x*g[t]]*(1 - f[t]^2); g = Table[ ExpandAll[(n!/3)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[ CoefficientList[(n!/3)*SeriesCoefficient[ FullSimplify[Series[p[t], {t, 0, 30}]], n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Sequence in context: A076600 A002978 A056460 this_sequence A117786 A117788 A006710
Adjacent sequences: A137520 A137521 A137522 this_sequence A137524 A137525 A137526
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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), Apr 24 2008
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