A023921 Theta series of A*_9 lattice.

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

0,10

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

S. Ahlgren, The sixth, eighth, ninth and tenth powers of Ramanujan's theta function, Proc. Amer. Math. Soc. 128 (2000), 1333-1338. [Expansion of F_10(q^2)]

G. Nebe and N. J. A. Sloane, Home page for this lattice

Example

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

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 *)

Crossrefs

Cf. A072836.

Sequence in context: A133591 A137643 A351570 * A072840 A091234 A221873

Adjacent sequences: A023918 A023919 A023920 * A023922 A023923 A023924

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved