A319310 Expansion of theta_4(q)^28 in powers of q = exp(Pi i t).

1, -56, 1512, -26208, 327656, -3147984, 24189984, -152867520, 811401192, -3681079640, 14500933104, -50376047904, 156797510688, -444306558864, 1163495873088, -2851049839680, 6597606440936, -14512424533488, 30505974273096, -61591664700384, 119983597365744, -226303038736128

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Simon Plouffe, Numbers in the base e^Pi, arXiv:2509.15609 [math.NT], 2025. See p. 16/24, marked 209.

Formula

Expansion of eta(q)^56 / eta(q^2)^28 in powers of q.

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/128) * Pi^7 / Gamma(3/4)^28 = A389038. - Simon Plouffe, Sep 22 2025

Crossrefs

theta_4(q)^b: A002448 (b=1), A104794 (b=2), A213384 (b=3), A096727 (b=4), A035016 (b=8), A286346 (b=12), A319307 (b=16), A319308 (b=20), A319309 (b=24), this sequence (b=28).

Sequence in context: A034202 A160290 A030649 * A022081 A017772 A233981

Adjacent sequences: A319307 A319308 A319309 * A319311 A319312 A319313

Keyword

sign

Author

Seiichi Manyama, Sep 16 2018

Status

approved