1,4

Row sums are:

{1, 2, 2, -4, -20, -8, 184, 464, -1648, -10720, 8224}

In real quantum mechanical 2 dimensional orthogonal partitions it would be:

p(x,y,n,m)=T(x,n)*H(y,m);

Here I have made x=y and n=m to get a new sort of polynomial with an

odd number of vector coefficients.

The traditional Schoedinger wave mechanics solution of hydrogen is a partition of four (not two dimensions):

wave_function=Bessel(r,n)*Legendre(theta,l)*Fourier(phi,m)*Spin(t,s)

p(x,n)=T(x,n)*H(x,n)

{1},

{0, 0, 2},

{2, 0, -8, 0, 8},

{0, 0, 36,0, -72, 0, 32},

{12, 0, -144, 0, 496, 0, -512, 0,128},

{0, 0, 600, 0, -3200, 0, 5280, 0, -3200, 0, 512},

{120, 0, -2880, 0, 19200, 0, -47104, 0, 47232, 0, -18432, 0, 2048},

{0, 0, 11760,0, -117600, 0, 385728, 0, -560000, 0,372736, 0, -100352, 0, 8192}, {1680, 0, -67200,0, 712320, 0, -3014144, 0, 5921024, 0, -5742592, 0, 2678784, 0, -524288, 0, 32768},

{0, 0, 272160, 0, -4354560, 0, 23175936, 0, -58143744, 0, 76202496,0, -52555776, 0, 17915904, 0, -2654208, 0, 131072},

{30240, 0, -1814400, 0, 27619200, 0, -175150080, 0, 546762240, 0, -919803904, 0, 860825600, 0, -439091200, 0, 113213440, 0, -13107200, 0, 524288}

Table[ExpandAll[ChebyshevT[n, x]*HermiteH[n, x]], {n, 0, 10}]; a = Table[CoefficientList[ChebyshevT[n, x]*HermiteH[n, x], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[ChebyshevT[n, x]*HermiteH[n, x], x]], {n, 0, 10}].

Cf. A053120, A060821.

Sequence in context: A104986 A060007 A021457 this_sequence A009187 A009803 A009615

Adjacent sequences: A137453 A137454 A137455 this_sequence A137457 A137458 A137459

tabl,uned,sign

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 18 2008