OFFSET
0,3
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of eta(q) * eta(q^2)^4 * eta(q^3) / eta(q^6)^2 in powers of q.
Euler transform of period 6 sequence [ -1, -5, -2, -5, -1, -4, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (24 t)) = 248832^(1/2) (t/I)^2 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A263021.
EXAMPLE
G.f. = 1 - x - 5*x^2 + 3*x^3 + 7*x^4 + 4*x^5 + 3*x^6 - 18*x^7 - 17*x^8 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ 2 q^(3/8) QPochhammer[ q] QPochhammer[ q^2]^4 / EllipticTheta[ 2, 0, q^(3/2)], {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^2 + A)^4 * eta(x^3 + A) / eta(x^6 + A)^2, n))};
CROSSREFS
KEYWORD
sign,look
AUTHOR
Michael Somos, Jan 02 2016
STATUS
approved