A286346 Expansion of eta(q)^24 / eta(q^2)^12 in powers of q.

1, -24, 264, -1760, 7944, -25872, 64416, -133056, 253704, -472760, 825264, -1297056, 1938336, -2963664, 4437312, -6091584, 8118024, -11368368, 15653352, -19822176, 24832944, -32826112, 42517728, -51425088, 61903776, -78146664, 98021616, -115331264, 133522752

Offset: 0

Author

Seiichi Manyama, May 08 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Simon Plouffe, Conjectures of the OEIS, as of June 20, 2018.

Crossrefs

Cf. A000145, A013973 (E_6).

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[((1 - x^k)/(1 + x^k))^12, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 10 2018 *)
a[n_] := (-1)^n SquaresR[12, n];
a /@ Range[0, 30] (* Jean-François Alcover, Feb 21 2021 *)

PARI

q = 'q + O('q^50); Vec(eta(q)^24 / eta(q^2)^12) \\ Michel Marcus, Jul 07 2018

Formula

a(n) = (-1)^n * A000145(n).

Euler Transform of [-24, -12, -24, -12, -24, -12, -24, -12, ...]. - Simon Plouffe, Jun 23 2018