1,1

Row sums are:

{2, 27, 484, 11280, 348456, 14589120, 819545280, 59538931200, 5399765562240, 596993441425920, 79100889171494400};

The atomic partition function ( Schodinger wave mechanic solution) is ( of the type):

P(x,y,z,t)=Bessel(x,n)*Fourier(y,m)*Legendre(z,l)*Spin(t,k)

That differential equation solution is basic quantum chemistry.

This partition is a projection of an {x,y,z} solution to a simple {x}.

That is why I call it "degenerate".

In the study of blackbody radiation "actual observation" there is a longer tail than the Bernoulli

distribution would predict ( actually a different curve shape).

That is what actually gave me this sort of idea.

Chebyshev is kind of special relativity velocity like with weight of 1/Sqrt[1-x^2].

Hermite is vibrator like/ oscillator with weight of Exp[ -x^2].

Bernoulli is "boson" like/ radiation and is used for most blackbody calculations

"classically". If you take the Hermite -Chebyshev as being a {3,1} type special relativity like system,

them the surface of a molecule behaving in a relativistic fashion would emit

photons by a partition like this...

This kind of thinking is what is called a physical "model" of a system.

1) b(x,t)=t*Exp(x*t)/(Exp(t)-1) 2) u(x,t)=1/(1-2*x*t+t^2) 3) h(x,t)=Exp(2*x*t-t^2) p(x,t)=b(x,t)*u(x,t)*h(x,t)=sum(P(x,n)*t^n/n!,{n,0,Infinity}); out_n,m=(n + 2)!*n!*Coefficients(P(x,n)).

{2},

{-3, 30},

{-92, -120, 696},

{720, -8340, -5220, 24120},

{40296, 103680, -722160, -289440, 1216080},

{-756000, 10579800, 13003200, -73306800, -21281400, 86350320},

{-71284800, -268531200, 2283140160, 1799884800, -9170280000, -2072407680,8319024000},

{2438553600, -41653241280, -75214137600, 512773208640, 294226732800, -1419973571520, -262049256000, 1048990642560},

{363233082240, 1780144128000, -18252909964800, -21270283776000, 128466991699200, 57669354086400, -269259449356800, -41959625702400, 167862311366400}, {-19615115520000, 402989255222400, 953596385280000, -7683295115865600, -6554013637248000, 36694836029617920, 13501295252121600, -61627138532467200, -8309184412636800, 33237523332921600},

{-4323226030502400, -25964377528320000, 313773569755430400, 482205929103360000, -3370903650930816000, -2258955163745280000, 12006293764671360000, 3739168341393408000, -16784976782008512000, -1994251399975296000, 7977033884466662400}

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

Sequence in context: A024631 A032814 A095927 this_sequence A110351 A088115 A048986

Adjacent sequences: A137978 A137979 A137980 this_sequence A137982 A137983 A137984

tabl,uned,sign

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 01 2008