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A231962
Expansion of b(q)^3 - (1/3)*c(q)^3 in powers of q where b(), c() are cubic AGM theta functions.
2
1, -18, 0, -90, -234, 0, -216, -900, 0, -738, -1296, 0, -1170, -3060, 0, -1728, -3690, 0, -2160, -6516, 0, -4500, -6480, 0, -3672, -10818, 0, -6570, -11700, 0, -6480, -17316, 0, -8640, -15552, 0, -9594, -24660, 0, -15300, -22032, 0, -10800, -33300, 0, -17280
OFFSET
0,2
COMMENTS
Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).
LINKS
FORMULA
Expansion of (eta(q)^3 / eta(q^3))^3 - 9 * q * (eta(q^3)^3 / eta(q))^3 in powers of q.
G.f. is a period 1 Fourier series which satisfies f(-1 / (3 t)) = - 3^(1/2) (t/i)^3 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A231961.
a(3*n + 2) = 0. a(3*n + 1) = -18 * A231947(n). a(3*n) = A231961(n).
EXAMPLE
G.f. = 1 - 18*q - 90*q^3 - 234*q^4 - 216*q^6 - 900*q^7 - 738*q^9 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[(eta[q]^3/ eta[q^3])^3 - 9*(eta[q^3]^3/eta[q])^3, {q, 0, 50}], q] (* G. C. Greubel, Aug 08 2018 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^3 / eta(x^3 + A))^3 - 9 * x * (eta(x^3 + A)^3 / eta(x + A))^3, n))}
CROSSREFS
Sequence in context: A289660 A096306 A335187 * A052441 A375665 A375681
KEYWORD
sign
AUTHOR
Michael Somos, Nov 15 2013
STATUS
approved