OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
FORMULA
Expansion of b(q^3)^3 - 3 * b(q) * c(q^3)^2 in powers of q where b(), c() are cubic AGM theta functions.
Expansion of b(q^3)^2 * (b(q) + c(q^3)) in powers of q^3 where b(), c() are cubic AGM theta functions.
Expansion of (eta(q)^9 + 9 * q * eta(q)^6 * eta(q^9)^3) / eta(q^3)^3 in powers of q.
a(3*n + 1) = 0. a(3*n) = A004007(n).
EXAMPLE
G.f. = 1 - 27*q^2 + 72*q^3 - 216*q^5 + 270*q^6 - 459*q^8 + 720*q^9 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[(eta[q]^9 + 9*q*eta[q]^6*eta[q^9]^3)/eta[q^3]^3, {q, 0, 50}], q] (* G. C. Greubel, Aug 11 2018 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^9 + 9 * x * eta(x + A)^6 * eta(x^9 + A)^3) / eta(x^3 + A)^3, n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Apr 04 2012
STATUS
approved