A319306 Expansion of (7 * theta_4(q)^20 * theta_2(q)^8 + 7 * theta_4(q)^24 * theta_2(q)^4 + 2 * theta_4(q)^28)/(2 * delta^2) in powers of q = exp(Pi i t), where delta is A000594.

1, 0, -232, 0, 86064, -1835008, 23619232, -229638144, 1841202076, -12765888512, 78856617456, -442924793856, 2295931514240, -11106754756608, 50583249259456, -218397947199488, 899050944837546, -3545383150551040, 13446464974112552, -49213617532305408

Offset

-4,3

Links

Seiichi Manyama, Table of n, a(n) for n = -4..10000

H. Cohn, A. Kumar, S. Miller, D. Radchenko, M. Viazovska, The sphere packing problem in dimension 24, Annals of Mathematics, 185 (3) (2017), 1017-1033.

Wikipedia, Sphere packing

Example

Let q = exp(Pi i t).
theta_2(q)^4 =     16*q          + 64*q^3 + ... .
theta_4(q)^4 = 1 -  8*q + 24*q^2 - 32*q^3 + ... .
delta = q^2 - 24*q^4 + 252*q^6 - 1472*q^8 + ... .
(7 * theta_4(q)^20 * theta_2(q)^8 + 7 * theta_4(q)^24 * theta_2(q)^4 + 2 * theta_4(q)^28)/delta^2
= 2*q^(-4) - 464*q^(-2) + 172128 - 3670016*q + 47238464*q^2 - 459276288*q^3 + ... .

Crossrefs

Cf. A000594, A007331, A008438 (theta_2(q)^4/(16*q)), A096727 (theta_4(q)^4), A319134, A319294, A319308 (theta_4(q)^20), A319309 (theta_4(q)^24), A319310 (theta_4(q)^28).

Sequence in context: A172908 A359011 A172935 * A280538 A050423 A126818

Adjacent sequences: A319303 A319304 A319305 * A319307 A319308 A319309

Keyword

sign

Author

Seiichi Manyama, Sep 16 2018

Status

approved