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Search: id:A137528
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| A137528 |
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A triangular sequence of coefficients based on an expansion of a Skew Catenoid of Matthius Weber like Sheffer expansion function: g(t) = x*(3 + t^2)/(t^2 - 1); f(t) = (3 + t^2)/(t^2 - 1); p(x,t) = Exp[x*(t)]*(1 - f(t)2). |
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1
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| -8, 0, -48, 0, 64, 0, -960, 0, 3072, 0, -1536, -40320, 0, 207360, 0, -230400, 0, 61440, 0, -2903040, 0, 20643840, 0, -36126720, 0, 20643840, 0, -3440640, 0, -319334400, 0, 2903040000, 0, -6967296000, 0, 6193152000, 0, -2167603200, 0, 247726080
(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:
{-8, 0, 16, 0, 576, 0, -1920, 0, -1182720, 0, -110315520}
Here is the relationship that seems to hold:
Weierstrass{f,g)-> Sheffer{g,fbar}.
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REFERENCES
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Bloomington's Virtual Minimal Surface Museum; Matthias Weber,http://www.indiana.edu/~minimal/toc.html Lecture 2.
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FORMULA
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g(t) = x*(3 + t^2)/(t^2 - 1); f(t) = (3 + t^2)/(t^2 - 1); p(x,t) = Exp[x*(t)]*(1 - f(t)2)=Sum(P(x,n)*t^n/n!,{n,0,Infinity}]; out_n,m=n!*Coefficients(P(x,n)/Exp[ -3*x^2).
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EXAMPLE
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{-8},
{0},
{-48, 0, 64},
{0},
{-960, 0, 3072, 0, -1536},
{},
{-40320, 0, 207360, 0, -230400, 0, 61440},
{0},
{-2903040, 0,20643840, 0, -36126720, 0, 20643840, 0, -3440640},
{0}, {-319334400, 0, 2903040000, 0, -6967296000, 0, 6193152000, 0, -2167603200, 0, 247726080}
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MATHEMATICA
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Clear[p, f, g] g[t_] = x*(3 + t^2)/(t^2 - 1); f[t] = (3 + t^2)/(t^2 - 1); p[t_] = Exp[x*g[t]]*(1 - f[t]^2); g = Table[ FullSimplify[ExpandAll[(n!)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]/Exp[ -3*x^2]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[ FullSimplify[Series[p[t], {t, 0, 30}]], n]/Exp[ -3*x^2], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Sequence in context: A088663 A011997 A047771 this_sequence A067817 A079137 A121770
Adjacent sequences: A137525 A137526 A137527 this_sequence A137529 A137530 A137531
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 24 2008
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