Euler transform of period 30 sequence [ 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 0, 4, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= u^2 -v -u*v*(2 + 4*v).
Expansion of (eta(q^2) * eta(q^6) * eta(q^10) * eta(q^30)) / (eta(q) * eta(q^3) * eta(q^5) * eta(q^15)) in powers of q.
G.f. is a period 1 Fourier series which satisfies f(-1 / (30 t)) = (1/4) g(t) where q = exp(2 Pi i t) and g() is the g.f. for
A132321.
G.f.: x * Product_{k>0} (1 + x^k) * (1 + x^(3*k)) * (1 + x^(5*k)) * (1 + x^(15*k)).
a(n) ~ exp(2*Pi*sqrt(2*n/15)) / (2^(11/4) * 15^(1/4) * n^(3/4)). -
Vaclav Kotesovec, Sep 07 2015
G.f.: r * s = (r + s - 1)/2 where r = x * Product_{k>0} (1 - x^(2*k)) * (1 - x^(30*k)) / ((1 - x^(3*k)) * (1 - x^(5*k))), s = Product_{k>0} (1 - x^(6*k)) * (1 - x^(10*k)) / ((1 - x^k) * (1 - x^(15*k))). -
Seiichi Manyama, May 05 2017
