1,2

Row sums = A032184.

But for an odd function of 2^n this might be a simple:

p[x,n]= -f(2^n)*((x+1)/(x-1))^n/n!;

The importance of these density curves is

that they are related to Mach's numbers for

velocity in a medium.

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:

F(pr)=(f(gamma)+pr)/(1+f(gamma)*pr).

A. M. Kuethe, J.D. Schetzer,Foundations of Aerodynamics, John Wiley and sons, Inc. New York,1959, page 180

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).

{-1},

{-2, -2},

{-4, -8, -4},

{-12, -36, -36, -12},

{-48, -192, -288, -192, -48},

{-240, -1200, -2400, -2400, -1200, -240},

{-1440, -8640, -21600, -28800, -21600, -8640, -1440},

{-10080, -70560, -211680, -352800, -352800, -211680, -70560, -10080},

{-80640, -645120, -2257920, -4515840, -5644800, -4515840, -2257920, -645120, -80640},

{-725760, -6531840, -26127360, -60963840, -91445760, -91445760, -60963840, -26127360, -6531840, -725760},

{-7257600, -72576000, -326592000, -870912000, -1524096000, -1828915200, -1524096000, -870912000, -326592000, -72576000, -7257600}

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}];

Cf. A007318, A032184.

Sequence in context: A121175 A038208 A116694 this_sequence A000017 A032522 A077964

Adjacent sequences: A137775 A137776 A137777 this_sequence A137779 A137780 A137781

tabl,uned,sign

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 28 2008