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, -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

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 * A369914 A291108 A117786

Adjacent sequences: A137520 A137521 A137522 * A137524 A137525 A137526

Keyword

uned,tabf,sign

Author

Roger L. Bagula, Apr 24 2008

Status

approved