

A137522


A triangular sequence from an expansion of coefficients of the function: p(x,t)=Exp(x*g*(t))*(1f(t)^2);f(t)=1/Sqrt[1  14*t^4 + t^8];g(t)=t. (Based on the Weierstrass functions of Schwarz's minimal surface which is identified with a cube.)


0



0, 0, 0, 0, 336, 0, 1680, 0, 0, 5040, 0, 0, 0, 11760, 7862400, 0, 0, 0, 23520, 0, 70761600, 0, 0, 0, 42336, 0, 0, 353808000, 0, 0, 0, 70560
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OFFSET

1,5


COMMENTS

Row sums: {0, 0, 0, 0, 336, 1680, 5040, 11760, 7885920, 70803936, 353878560}.
Because of the 8th power in generator function nothing shows up until n=5 and then the secondary polynomial doesn't show up until the 9th power.


LINKS



FORMULA

p(x,t)=Exp(x*g*(t))*(1f(t)^2);f(t)=1/Sqrt[1  14*t^4 + t^8];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},
{0},
{0},
{336},
{0, 1680},
{0, 0, 5040},
{0, 0, 0, 11760},
{7862400, 0, 0, 0, 23520},
{0, 70761600, 0, 0, 0, 42336},
{0, 0, 353808000, 0, 0, 0, 70560}


MATHEMATICA

Clear[p, f, g] g[t_] = t; f[t] = 1/Sqrt[1  14*t^4 + t^8]; 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



KEYWORD

uned,tabf,sign


AUTHOR



STATUS

approved



