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 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). 0
 -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 (list; table; graph; refs; listen; history; text; internal format)
 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 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

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Last modified March 24 15:37 EDT 2023. Contains 361479 sequences. (Running on oeis4.)