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Search: id:A137520
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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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| -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
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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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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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)=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: A092173 A062521 A099645 this_sequence A010676 A071873 A036478
Adjacent sequences: A137517 A137518 A137519 this_sequence A137521 A137522 A137523
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 24 2008
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