A137520 A triangular sequence from an expansion of coefficients of the function: p(x,t)=Exp(x*g*(t))*(1-f(t)^2);f(t)=4/(t^4-1);g(t)=t. (based on the Weierstrass functions of Scherk's minimal surface).

-5, 0, -5, 0, 0, -5, 0, 0, 0, -5, -256, 0, 0, 0, -5, 0, -1280, 0, 0, 0, -5, 0, 0, -3840, 0, 0, 0, -5, 0, 0, 0, -8960, 0, 0, 0, -5, -645120, 0, 0, 0, -17920, 0, 0, 0, -5, 0, -5806080, 0, 0, 0, -32256, 0, 0, 0, -5, 0, 0, -29030400, 0, 0, 0, -53760, 0, 0, 0, -5

Offset

1,1

Comments

Row sums: {-5, -5, -5, -5, -261, -1285, -3845, -8965, -663045, -5838341, -29084165}.

A n!/3 factor was used to lower the integer values of the coefficients.

The secondary polynomial doesn't show up until the 5th power.

Links

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

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)=4/(t^4-1);g(t)=t; p(x,t)=Sum[P(x,n)*t^n/n!,{n,0,Infinity}]; Out_n,m=(n!/3)*Coefficients(P(x,n).

Example

{-5},
{0, -5},
{0, 0, -5},
{0, 0, 0, -5},
{-256, 0, 0, 0, -5},
{0, -1280, 0, 0, 0, -5},
{0, 0, -3840, 0, 0, 0, -5},
{0, 0, 0, -8960,0, 0, 0, -5},
{-645120, 0, 0, 0, -17920, 0, 0, 0, -5},
{0, -5806080, 0, 0, 0, -32256, 0, 0, 0, -5},
{0, 0, -29030400, 0, 0, 0, -53760, 0, 0, 0, -5}

Mathematica

Clear[p, f, g] g[t_] = t; f[t] = 4/(t^4 - 1); 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: A220412 A199092 A167260 * A010676 A071873 A036478

Adjacent sequences: A137517 A137518 A137519 * A137521 A137522 A137523

Keyword

uned,tabl,sign

Author

Roger L. Bagula, Apr 24 2008

Status

approved