Let t(q) = (eta(q)/eta(q^3))^12 = 1/q-12+54q-76q^2-243q^3+.... If j(q) is the j-invariant, with q-series given by A000521, then j(q) = (t+27)(t+243)^3/t^3 j(q^3) = (t+27)(t+3)^3/t. Hence t(q) can be used to parametrize the classical modular curve X0(3). - Gene Ward Smith, Aug 04 2006
Expansion of (eta(q) / eta(q^3))^12 in powers of q.
Expansion of (3 * b(q) / c(q))^3 in powers of q where b(), c() are cubic AGM theta functions. - Michael Somos, Jun 16 2012
Euler transform of period 3 sequence [ -12, -12, 0, ...]. - Michael Somos, Nov 08 2011
G.f. A(q) satisfies 0 = f(A(q), A(q^2)) where f(u, v) = (u + v)^3 - u * (27 + u) * v * (27 + v). - Michael Somos, Nov 08 2011
G.f. is a period 1 Fourier series which satisfies f(-1 / (3 t)) = 729 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A121590. - Michael Somos, Nov 08 2011
Convolution inverse of A121590. Convolution square of A007262. Convolution cube of A058095. Convolution fourth power of A199659. Convolution sixth power of A112157. Convolution twelfth power of A137569.
a(-1) = 1, a(n) = -(12/(n+1))*Sum_{k=1..n+1} A046913(k)*a(n-k) for n > -1. - Seiichi Manyama, Mar 29 2017
