A319307 Expansion of theta_4(q)^16 in powers of q = exp(Pi i t).

1, -32, 480, -4480, 29152, -140736, 525952, -1580800, 3994080, -8945824, 18626112, -36714624, 67978880, -118156480, 197120256, -321692928, 509145568, -772845120, 1143441760, -1681379200, 2428524096, -3392205824, 4658843520, -6411152640, 8705492608, -11488092896

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)^32 / eta(q^2)^16 in powers of q.

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/16) * Pi^4 / Gamma(3/4)^16 = A389035. - 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), this sequence (b=16), A319308 (b=20), A319309 (b=24), A319310 (b=28).

Cf. A000152.

Sequence in context: A282525 A250319 A000152 * A022069 A250560 A203720

Adjacent sequences: A319304 A319305 A319306 * A319308 A319309 A319310

Keyword

sign

Author

Seiichi Manyama, Sep 16 2018

Status

approved