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 A137522 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.) 0

%I

%S 0,0,0,0,-336,0,-1680,0,0,-5040,0,0,0,-11760,-7862400,0,0,0,-23520,0,

%T -70761600,0,0,0,-42336,0,0,-353808000,0,0,0,-70560

%N 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.)

%C Row sums: {0, 0, 0, 0, -336, -1680, -5040, -11760, -7885920, -70803936, -353878560}.

%C 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.

%H Francisco J. Lopez, Francisco Martin, <a href="http://www.ugr.es/~fmartin/complete_minimal_surfaces_in_r3.htm">Complete minimal surfaces in R^3</a>, April 11, 2000, web pdf, page 11.

%F 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).

%e {0},

%e {0},

%e {0},

%e {0},

%e {-336},

%e {0, -1680},

%e {0, 0, -5040},

%e {0, 0, 0, -11760},

%e {-7862400, 0, 0, 0, -23520},

%e {0, -70761600, 0, 0, 0, -42336},

%e {0, 0, -353808000, 0, 0, 0, -70560}

%t 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]

%K uned,tabf,sign

%O 1,5

%A _Roger L. Bagula_, Apr 24 2008

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Last modified June 12 06:52 EDT 2021. Contains 344943 sequences. (Running on oeis4.)