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 f(-x)^3 / chi(-x) = f(-x^2)^3 * chi(-x)^2 = phi(-x) * f(-x^2)^2 in powers of x where phi(), chi(), f() are Ramanujan theta functions.
Euler transform of period 2 sequence [ -2, -3, ...].
G.f.: Product_{k>0} (1 - x^k)^2 * (1 - x^(2*k)).
Convolution square is A230280.
EXAMPLE
G.f. = 1 - 2*x - 2*x^2 + 4*x^3 + x^4 + 2*x^5 - 2*x^6 - 4*x^7 - x^8 + ...
G.f. = q - 2*q^7 - 2*q^13 + 4*q^19 + q^25 + 2*q^31 - 2*q^37 - 4*q^43 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x]^2 QPochhammer[ x^2], {x, 0, n}];
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^2 + A), n))};
(PARI) q='q+O('q^99); Vec(eta(q)^2*eta(q^2)) \\ Altug Alkan, Apr 18 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 18 2013
EXTENSIONS
Terms and offset corrected by Joerg Arndt, Oct 21 2013
STATUS
approved