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A137526 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). 0
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; text; internal format)
OFFSET

1,4

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}.

LINKS

Table of n, a(n) for n=1..66.

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)).

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}

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]

CROSSREFS

Sequence in context: A318361 A078924 A229141 * A137525 A166335 A109187

Adjacent sequences:  A137523 A137524 A137525 * A137527 A137528 A137529

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Apr 24 2008

STATUS

approved

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Last modified October 18 11:56 EDT 2018. Contains 316321 sequences. (Running on oeis4.)