1,3

Row sums are:

{1, 7, 19, 133, 541, 4411, 23647, 248809, 1705753, 22398031, 187640971};

This function is called Samuel Lattes' function by Mandelbrot

and it's inverse in Hill is Onsager's k1 associated with the two dimensional

crystal. I have exchanged the constant in each of these equations for an Exp[x*t]

to get my expansion function. The dynamics associated with this function are

chaotic. It also seems to be strongly associated with the magnetization

function A136264.

The Beauty of Fractals, Springer-Verlag, New York, 1986, editors Peitgen and Richter, pages 153

Terrell Hill, Statistical Mechanics, Dover, 1987, page 329 ff

p(x,t)=Exp[x*t]*(1 + t^2)^2/(t*(1 - t^2))=Sum(P(x,n)8t^n/n1,{n,0,Infinity}); out_n,m=(n+1)!*Coefficient(P(x,n)).

{0, 1},

{6, 0, 1},

{0, 18, 0, 1},

{96, 0, 36, 0, 1},

{0, 480, 0, 60, 0, 1},

{2880, 0, 1440, 0, 90, 0, 1},

{0, 20160, 0, 3360, 0, 126, 0, 1},

{161280, 0, 80640, 0, 6720, 0, 168, 0, 1},

{0, 1451520, 0, 241920, 0, 12096, 0, 216, 0, 1},

{14515200, 0, 7257600, 0, 604800, 0, 20160, 0, 270, 0, 1},

{0, 159667200, 0, 26611200, 0, 1330560, 0, 31680, 0, 330, 0, 1}

p[t_] = Exp[x*t]*(1 + t^2)^2/(t*(1 - t^2)); Table[ ExpandAll[(n + 1)!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], { n, 0, 10}]; a = Table[(n + 1)!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]

Cf. A136264.

Sequence in context: A137378 A084680 A051626 this_sequence A134899 A076413 A154305

Adjacent sequences: A137782 A137783 A137784 this_sequence A137786 A137787 A137788

nonn,tabl,uned

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