OFFSET
-1,3
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..1000
J. M. Borwein and P. B. Borwein, A cubic counterpart of Jacobi's identity and the AGM, Trans. Amer. Math. Soc., 323 (1991), no. 2, 691-701.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of c(q) / c(q^4) in powers of q where c() is a cubic AGM function.
Expansion of eta(q^3)^3 * eta(q^4) / (eta(q) * eta(q^12)^3) in powers of q.
Euler transform of period 12 sequence [ 1, 1, -2, 0, 1, -2, 1, 0, -2, 1, 1, 0, ...].
Convolution inverse of A123649.
a(2*n) = 0 unless n=0. a(2*n - 1) = A058487(n).
EXAMPLE
G.f. = 1/q + 1 + 2*q + q^3 - 2*q^7 - 2*q^9 + 2*q^11 + 4*q^13 + 3*q^15 - 4*q^17 + ...
MATHEMATICA
QP = QPochhammer; s = QP[q^3]^3*(QP[q^4]/(QP[q]*QP[q^12]^3)) + O[q]^80; CoefficientList[s, q] (* Jean-François Alcover, Nov 16 2015, adapted from PARI *)
PROG
(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^3 + A)^3 * eta(x^4 + A) / (eta(x + A) * eta(x^12 + A)^3), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Mar 05 2011
STATUS
approved