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A023921 Theta series of A*_9 lattice. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,10
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 114.
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 18 18:14 EDT 2024. Contains 373486 sequences. (Running on oeis4.)