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A137526
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A triangular sequence of coefficients based on an expansion of a Enneper like Sheffer expansion function: g(t) = t; f(t) = t; p(x,t) = Exp[x*(t)]*(1 - f(t)2).
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0
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1, 0, 1, -2, 0, 1, 0, -6, 0, 1, 0, 0, -12, 0, 1, 0, 0, 0, -20, 0, 1, 0, 0, 0, 0, -30, 0, 1, 0, 0, 0, 0, 0, -42, 0, 1, 0, 0, 0, 0, 0, 0, -56, 0, 1, 0, 0, 0, 0, 0, 0, 0, -72, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -90, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Row sums:
{1, 1, -1, -5, -11, -19, -29, -41, -55, -71, -89};
Here is the relationship that seems to hold:
Weierstrass{f,g)-> Sheffer{g,fbar}.
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FORMULA
| g(t) = t; f(t) = t; 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)).
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EXAMPLE
| {1},
{0, 1},
{-2, 0, 1},
{0, -6, 0, 1},
{0, 0, -12, 0, 1},
{0, 0, 0, -20, 0, 1},
{0, 0, 0, 0, -30, 0, 1},
{0, 0, 0, 0, 0, -42, 0, 1},
{0, 0, 0, 0, 0, 0, -56, 0, 1},
{0, 0, 0, 0, 0, 0, 0, -72, 0, 1},
{0, 0, 0, 0, 0, 0, 0, 0, -90, 0, 1}
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MATHEMATICA
| Clear[p, f, g] g[t_] = t; f[t] = t; p[t_] = Exp[x*g[t]]*(1 - f[t]^2); g = Table[ FullSimplify[ExpandAll[(n!)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], {n, 0, 10}]; a = Table[ CoefficientList[n!*SeriesCoefficient[ FullSimplify[Series[p[t], {t, 0, 30}]], n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
| Sequence in context: A128890 A196777 A078924 * A137525 A166335 A109187
Adjacent sequences: A137523 A137524 A137525 * A137527 A137528 A137529
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KEYWORD
| uned,tabl,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 24 2008
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