A319308 Expansion of theta_4(q)^20 in powers of q = exp(Pi i t).

1, -40, 760, -9120, 77560, -497648, 2508000, -10232640, 34729720, -100906760, 259114704, -606957280, 1327461600, -2738111280, 5341699520, -9915552192, 17701924600, -30615844560, 51294999960, -83279292960, 131880275664, -204949382400, 312126610080, -464844224960, 680432137440

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)^40 / eta(q^2)^20 in powers of q.

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/32) * Pi^5 / Gamma(3/4)^20 = A389036. - 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), this sequence (b=20), A319309 (b=24), A319310 (b=28).

Sequence in context: A010840 A233725 A175603 * A022073 A261571 A010956

Adjacent sequences: A319305 A319306 A319307 * A319309 A319310 A319311

Keyword

sign

Author

Seiichi Manyama, Sep 16 2018

Status

approved