OFFSET
0,25
COMMENTS
LINKS
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(1/6) * (eta(q) * eta(q^6)^2) / (eta(q^2) * eta(q^3) * eta(q^12)) in powers of q.
Euler transform of period 12 sequence [-1, 0, 0, 0, -1, -1, -1, 0, 0, 0, -1, 0, ...].
G.f.: Product_{k>=1} (1 - x^(2*k-1)) * (1 + x^(6*k-3)).
EXAMPLE
G.f. = 1 - x - x^5 + x^8 + x^12 - x^13 + x^16 - x^17 + x^20 + ...
G.f. = q^-1 - q^5 - q^29 + q^47 + q^71 - q^77 + q^95 - q^101 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x, x^2] QPochhammer[ -x^3, x^6], {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n < 0, 0, A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^6 + A)^2) / (eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 27 2019
STATUS
approved