This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A137778 #6 Jul 25 2013 12:57:37
%S A137778 -1,-2,-2,-4,-8,-4,-12,-36,-36,-12,-48,-192,-288,-192,-48,-240,-1200,
%T A137778 -2400,-2400,-1200,-240,-1440,-8640,-21600,-28800,-21600,-8640,-1440,
%U A137778 -10080,-70560,-211680,-352800,-352800,-211680,-70560,-10080,-80640,-645120,-2257920,-4515840,-5644800,-4515840
%N A137778 Triangular sequence from coefficients of an expansion of a Rankine-Hugoniot relation function for density in terms of thermodynamic gamma as t and pressure ratio as x: p(x,t)=((t + 1)/(t - 1) + x)/(1 + (t + 1)*x/(t - 1)).
%C A137778 Row sums = A032184.
%C A137778 But for an odd function of 2^n this might be a simple:
%C A137778 p[x,n]= -f(2^n)*((x+1)/(x-1))^n/n!.
%C A137778 The importance of these density curves is that they are related to Mach's numbers for velocity in a medium.
%C A137778 It also seems important that the equation has a Moebius form that is Blaschke/ Elliptic in shape in terms of gamma and pressure ratio pr:
%C A137778 F(pr)=(f(gamma)+pr)/(1+f(gamma)*pr).
%D A137778 A. M. Kuethe, J.D. Schetzer, Foundations of Aerodynamics, John Wiley and sons, Inc. New York,1959, page 180
%F A137778 p(x,t)=((t + 1)/(t - 1) + x)/(1 + (t + 1)*x/(t -1))=Sum(Q(x,n)*t^n/n!,{n,0,Infinity}]; out_n,m]=n!*(1 - x)^(n))*Coefficient(Q(x,n).
%e A137778 {-1},
%e A137778 {-2, -2},
%e A137778 {-4, -8, -4},
%e A137778 {-12, -36, -36, -12},
%e A137778 {-48, -192, -288, -192, -48},
%e A137778 {-240, -1200, -2400, -2400, -1200, -240},
%e A137778 {-1440, -8640, -21600, -28800, -21600, -8640, -1440},
%e A137778 {-10080, -70560, -211680, -352800, -352800, -211680, -70560, -10080},
%e A137778 {-80640, -645120, -2257920, -4515840, -5644800, -4515840, -2257920, -645120, -80640},
%e A137778 {-725760, -6531840, -26127360, -60963840, -91445760, -91445760, -60963840, -26127360, -6531840, -725760},
%e A137778 {-7257600, -72576000, -326592000, -870912000, -1524096000, -1828915200, -1524096000, -870912000, -326592000, -72576000, -7257600}
%t A137778 p[t_] = ((t + 1)/(t - 1) + x)/(1 + (t + 1)*x/(t - 1)); Table[ExpandAll[ FullSimplify[(n!*(1 - x)^(n))*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], {n, 0, 10}]; a = Table[ CoefficientList[ExpandAll[ FullSimplify[(n!*(1 - x)^(n))*SeriesCoefficient[Series[p[t], {t, 0, 30}], n]]], x], {n, 0, 10}]; Flatten[a] Table[ Apply[Plus, CoefficientList[ExpandAll[ FullSimplify[(n!*(1 - x)^(n))*SeriesCoefficient[Series[p[t], {t, 0, 30}], n]]], x]], {n, 0, 10}];
%Y A137778 Cf. A007318, A032184.
%K A137778 tabl,uned,sign
%O A137778 1,2
%A A137778 _Roger L. Bagula_, Apr 28 2008