cp's OEIS Frontend

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.

A023921 Theta series of A*_9 lattice.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 90, 240, 0, 0, 420, 252, 0, 0, 0, 720, 0, 0, 0, 0, 0, 0, 1700, 0, 0, 0, 1260, 2700, 0, 0, 3240, 1680, 0, 0, 0, 5220, 0, 0, 0, 0, 0, 0, 7740, 0, 0, 0, 4920, 10080, 0, 0, 12690, 7020, 0, 0, 0, 15120, 0, 0, 0, 0, 0
Offset: 0

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Examples

			G.f. = 1 + 20*q^9 + 90*q^16 + 90*q^20 + 240*q^21 + 420*q^24 + 252*q^25 + 720*q^29 + 1700*q^36 + 1260*q^40 + .... - _G. C. Greubel_, Apr 16 2018
		

References

  • J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 114.

Crossrefs

Cf. A072836.

Programs

  • Mathematica
    f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; F[10,q_]:= f[q^5, q^5]^10/f[q, q] - 8*q^2*f[q^5, q^5]^5* QPochhammer[q^10]^5/QPochhammer[q^2] - (27*q^4*f[q^5, q^5]^5 - 125*q^9*f[q^5, q^5]*f[q^10, q^30]^4 + 5*q^5*f[q^5, q^5]*f[q^2, q^6]^4)* QPochhammer[q^20]^5/QPochhammer[q^4] - 17*q^5*f[q, q]*f[q^5, q^15]^8 + 2*q*f[q, q]*f[q^5, q^5]^4*f[q^2, q^6]^4 - 20*q^8*f[q, q]*QPochhammer[q^20]^10/QPochhammer[q^4]^2 + 5*q^4*f[q, q]*QPochhammer[q^10]^10/QPochhammer[q^2]^2; CoefficientList[Series[F[10, q], {q, 0, 100}], q] (* G. C. Greubel, Apr 16 2018 *)