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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
 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; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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. LINKS Table of n, a(n) for n=1..32. Francisco J. Lopez, Francisco Martin, Complete minimal surfaces in R^3, April 11, 2000, web pdf, page 11. FORMULA 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). EXAMPLE {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} MATHEMATICA 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] CROSSREFS Sequence in context: A204612 A204796 A348822 * A090487 A289220 A060664 Adjacent sequences: A137519 A137520 A137521 * A137523 A137524 A137525 KEYWORD uned,tabf,sign AUTHOR Roger L. Bagula, Apr 24 2008 STATUS approved

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Last modified December 7 21:37 EST 2023. Contains 367662 sequences. (Running on oeis4.)