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Search: id:A137522
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| A137522 |
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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 - 14*t^4 + t^8];g(t)=t. (based on the Weierstrass functions of Schwarz's minimal surface which is identified with a cube). |
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1
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| 0, 0, 0, 0, -336, 0, -1680, 0, 0, -5040, 0, 0, 0, -11760, -7862400, 0, 0, 0, -23520, 0, -70761600, 0, 0, 0, -42336, 0, 0, -353808000, 0, 0, 0, -70560
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums:
{0, 0, 0, 0, -336, -1680, -5040, -11760, -7885920, -70803936, -353878560}
Because of the 8th power in generator function nothing shows up until n=5
and then the secondary polynomial doesn't show up until the 9th power.
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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 11
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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 - 14*t^4 + t^8];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},
{0},
{0},
{-336},
{0, -1680},
{0, 0, -5040},
{0, 0, 0, -11760},
{-7862400, 0, 0, 0, -23520},
{0, -70761600, 0, 0, 0, -42336},
{0, 0, -353808000, 0, 0, 0, -70560}
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MATHEMATICA
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Clear[p, f, g] g[t_] = t; f[t] = 1/Sqrt[1 - 14*t^4 + t^8]; 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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Adjacent sequences: A137519 A137520 A137521 this_sequence A137523 A137524 A137525
Sequence in context: A046015 A105099 A038648 this_sequence A090487 A060664 A064259
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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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