OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(-2/3) * eta(q)^4 * eta(q^6)^3 / eta(q^2)^3 in powers of q.
Euler transform of period 6 sequence [ -4, -1, -4, -1, -4, -4, ...].
3 * a(n) = A260301(3*n + 2).
EXAMPLE
G.f. = 1 - 4*x + 5*x^2 - 4*x^3 + 10*x^4 - 16*x^5 + 12*x^6 - 8*x^7 + ...
G.f. = q^2 - 4*q^5 + 5*q^8 - 4*q^11 + 10*q^14 - 16*q^17 + 12*q^20 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x] QPochhammer[ x, x^2]^2 QPochhammer[ x^6]^3, {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^4 * eta(x^6 + A)^3 / eta(x^2 + A)^3, n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Dec 09 2016
STATUS
approved