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 (eta(q) / eta(q^2))^5 * eta(q^10) / eta(q^5) in powers of q.
Euler transform of period 10 sequence [ -5, 0, -5, 0, -4, 0, -5, 0, -5, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = v * ((u+1)^2 + v) - (v + 4 * u).
G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u - v)^4 - u * v * (u - 1) * (u + 4) * (v - 1) * (v + 4).
G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = 4 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A095813.
G.f.: Product_{k>0} (1 + x^(5*k)) / (1 + x^k)^5.
a(n) = (-1)^n * A225701(n). - Michael Somos, Sep 15 2015
EXAMPLE
G.f. = 1 - 5*q + 10*q^2 - 15*q^3 + 30*q^4 - 55*q^5 + 80*q^6 - 120*q^7 + 190*q^8 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ -q^5, q^5] / QPochhammer[ -q, q]^5, {q, 0, n}]; (* Michael Somos, Sep 15 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( ( eta(x + A) / eta(x^2 + A) )^5 * eta(x^10 + A) / eta(x^5 + A), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Mar 23 2008
STATUS
approved