The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 12 06:35 EDT 2024. Contains 374237 sequences. (Running on oeis4.)