OFFSET
0,7
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 (eta(q^2) / eta(q^5))^3 * eta(q^10) / eta(q) in powers of q.
Euler transform of period 10 sequence [ 1, -2, 1, -2, 4, -2, 1, -2, 1, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u - v)^2 - u * (u + 4) * (1 - v).
G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u-v)^4 - u * (1 - u) * (4 + u) * v * (1 - v) * (4 + v).
G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = (5/4) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A138520.
G.f.: Product_{k>0} P(2, x^k)^4 * P(10, x^k) / P(5, x^k)^2 where P(n, x) is the n-th cyclotomic polynomial.
EXAMPLE
G.f. = 1 + q - q^2 - q^4 + q^5 + 4*q^6 - 4*q^7 - q^8 - 3*q^9 + 3*q^10 + 12*q^11 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (QPochhammer[ q^2] / QPochhammer[ q^5])^3 QPochhammer[ q^10] / QPochhammer[ q], {q, 0, n}]; (* Michael Somos, Sep 14 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^10 + A) / eta(x + A) * ( eta(x^2 + A) / eta(x^5 + A) )^3, n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Mar 23 2008
STATUS
approved