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A137523 A triangular sequence from an expansion of coefficients of the function: p(x,t)=Exp(x*g*(t))*(1-f(t)^2);f(t)=1/Sqrt[1 - 2*t^2 + t^4];g(t)=t. (Based on the Weierstrass functions of Jenkins-Serrin minimal surface.) 0
0, 0, -4, 0, -12, -72, 0, -24, 0, -360, 0, -40, -2880, 0, -1080, 0, -60, 0, -20160, 0, -2520, 0, -84, -201600, 0, -80640, 0, -5040, 0, -112, 0, -1814400, 0, -241920, 0, -9072, 0, -144, -21772800, 0, -9072000, 0, -604800, 0, -15120, 0, -180 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row sums: {0, 0, -4, -12, -96, -400, -4020, -22764, -287392, -2065536, -31464900}.

Because of the 4th power in generator function nothing shows up until n=3.

LINKS

Table of n, a(n) for n=1..47.

Francisco J. Lopez, Francisco Martin, Complete minimal surfaces in R^3, April 11 2000, see pdf page 11

FORMULA

p(x,t)=Exp(x*g*(t))*(1-f(t)^2);f(t)=1/Sqrt[1 - 2*t^2 + t^4];g(t)=t; p(x,t)=Sum[P(x,n)*t^n/n!,{n,0,Infinity}]; Out_n,m=(n!)*Coefficients(P(x,n).

EXAMPLE

{0},

{0},

{-4},

{0, -12},

{-72, 0, -24},

{0, -360,0, -40},

{-2880, 0, -1080, 0, -60},

{0, -20160, 0, -2520, 0, -84},

{-201600, 0, -80640, 0, -5040, 0, -112},

{0, -1814400, 0, -241920, 0, -9072, 0, -144},

{-21772800, 0, -9072000, 0, -604800, 0, -15120, 0, -180}

MATHEMATICA

Clear[p, f, g] g[t_] = t; f[t] = 1/Sqrt[1 - 2*t^2 + t^4]; 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]

CROSSREFS

Sequence in context: A273682 A170878 A056460 * A291108 A117786 A117788

Adjacent sequences:  A137520 A137521 A137522 * A137524 A137525 A137526

KEYWORD

uned,tabf,sign

AUTHOR

Roger L. Bagula, Apr 24 2008

STATUS

approved

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Last modified June 12 08:13 EDT 2021. Contains 344943 sequences. (Running on oeis4.)