A319294 - OEIS

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A319294

Expansion of 128 * ((theta_3(q)^4 + theta_4(q)^4)/theta_2(q)^8 + (theta_4(q)^4 - theta_2(q)^4)/theta_3(q)^8) in powers of q = exp(Pi i t).

1, 0, 144, -5120, 70524, -626688, 4265600, -24164352, 119375370, -529539072, 2151757440, -8125793280, 28827864296, -96885780480, 310514729472, -954123868160, 2823202073655, -8074060259328, 22387521828480, -60344692402176, 158484892943628, -406368240128000, 1019049374174976

(list; graph; refs; listen; history; text; internal format)

OFFSET

-2,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = -2..10000

Maryna S. Viazovska, The sphere packing problem in dimension 8, arXiv preprint arXiv:1603.04246 [math.NT], 2016.

EXAMPLE

Let q = exp(Pi i t).

theta_2(q)^4 = 16*q + 64*q^3 + ... .

theta_3(q)^4 = 1 + 8*q + 24*q^2 + 32*q^3 + ... .

theta_4(q)^4 = 1 - 8*q + 24*q^2 - 32*q^3 + ... .

128 * (theta_3(q)^4 + theta_4(q)^4)/theta_2(q)^8