OFFSET
0,3
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 phi(-x^3) * f(-x^4)^2 / f(-x) in powers of x where phi(), f() are Ramanujan theta functions.
Expansion of q^(-7/24) * eta(q^3)^2 * eta(q^4)^2 / (eta(q) * eta(q^6)) in powers of q.
Euler transform of period 12 sequence [ 1, 1, -1, -1, 1, 0, 1, -1, -1, 1, 1, -2, ...].
G.f.: Product_{k>0} (1 + x^(2*k)) * (1 - x^(3*k)) * (1 - x^(4*k)) / (1 - x^k + x^(2*k)).
EXAMPLE
G.f. = 1 + x + 2*x^2 + x^3 + x^4 + x^5 + x^6 + 3*x^7 + x^8 + x^9 + ...
G.f. = q^7 + q^31 + 2*q^55 + q^79 + q^103 + q^127 + q^151 + 3*q^175 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^3]^2 QPochhammer[ x^4]^2 / (QPochhammer[ x] QPochhammer[ x^6]), {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A)^2 * eta(x^4 + A)^2 / (eta(x + A) * eta(x^6 + A)), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jul 15 2015
STATUS
approved