OFFSET
0,2
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
Amanda Clemm, Modular Forms and Weierstrass Mock Modular Forms, Mathematics, volume 4, issue 1, (2016)
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q * eta(q^12)^10 * eta(q^36)^6 / (eta(q^6)^3 * eta(q^18)^3 * eta(q^24)^3 * eta(q^72)^3) in powers of q^6.
Euler transform of period 12 sequence [3, -7, 6, -4, 3, -10, 3, -4, 6, -7, 3, -4, ...].
a(n) = (-1)^n * A280328(n).
EXAMPLE
G.f. = 1 + 3*x - x^2 - 5*x^3 + 8*x^4 - x^5 - 28*x^6 + 11*x^7 + 10*x^8 + ...
G.f. = q^-1 + 3*q^5 - q^11 - 5*q^17 + 8*q^23 - q^29 - 28*q^35 + 11*q^41 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ -x]^3 QPochhammer[ x^2] QPochhammer[ -x^3, x^6]^3, {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^10 * eta(x^6 + A)^6 / (eta(x + A)^3 * eta(x^3 + A)^3 * eta(x^4 + A)^3 * eta(x^12 + A)^3), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jan 01 2017
STATUS
approved