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A137520
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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)=4/(t^4-1);g(t)=t. (based on the Weierstrass functions of Scherk's minimal surface).
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0
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-5, 0, -5, 0, 0, -5, 0, 0, 0, -5, -256, 0, 0, 0, -5, 0, -1280, 0, 0, 0, -5, 0, 0, -3840, 0, 0, 0, -5, 0, 0, 0, -8960, 0, 0, 0, -5, -645120, 0, 0, 0, -17920, 0, 0, 0, -5, 0, -5806080, 0, 0, 0, -32256, 0, 0, 0, -5, 0, 0, -29030400, 0, 0, 0, -53760, 0, 0, 0, -5
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OFFSET
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1,1
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COMMENTS
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Row sums: {-5, -5, -5, -5, -261, -1285, -3845, -8965, -663045, -5838341, -29084165}.
A n!/3 factor was used to lower the integer values of the coefficients.
The secondary polynomial doesn't show up until the 5th power.
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LINKS
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Table of n, a(n) for n=1..66.
Francisco J. Lopez, Francisco Martin, Complete minimal surfaces in R^3, April 11 2000, see 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)=4/(t^4-1);g(t)=t; p(x,t)=Sum[P(x,n)*t^n/n!,{n,0,Infinity}]; Out_n,m=(n!/3)*Coefficients(P(x,n).
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EXAMPLE
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{-5},
{0, -5},
{0, 0, -5},
{0, 0, 0, -5},
{-256, 0, 0, 0, -5},
{0, -1280, 0, 0, 0, -5},
{0, 0, -3840, 0, 0, 0, -5},
{0, 0, 0, -8960,0, 0, 0, -5},
{-645120, 0, 0, 0, -17920, 0, 0, 0, -5},
{0, -5806080, 0, 0, 0, -32256, 0, 0, 0, -5},
{0, 0, -29030400, 0, 0, 0, -53760, 0, 0, 0, -5}
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MATHEMATICA
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Clear[p, f, g] g[t_] = t; f[t] = 4/(t^4 - 1); 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: A220412 A199092 A167260 * A010676 A071873 A036478
Adjacent sequences: A137517 A137518 A137519 * A137521 A137522 A137523
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula, Apr 24 2008
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STATUS
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approved
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