OFFSET
-1,4
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = -1..10000
FORMULA
Expansion of q^(-1) * chi(-q^5)^5 / chi(-q) in powers of q where chi() is a Ramanujan theta function.
Expansion of (eta(q^5) / eta(q^10))^5 / (eta(q) / eta(q^2)) in powers of q.
Euler transform of period 10 sequence [ 1, 0, 1, 0, -4, 0, 1, 0, 1, 0, ...].
G.f. A(q) satisfies A(q^2) = - A(q) * A(-q). - Michael Somos, Jul 05 2014
G.f. A(q) satisfies 0 = f(A(q), A(q^2)) where f(u, v) = u^2 * v - v^2 - 4 * u - 2 * u * v.
G.f. A(q) satisfies 0 = f(A(q), A(q^3)) where f(u, v) = (u - v)^4 - u * v * (u^2 - 3 * u - 4) * (v^2 - 3 * 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 A132985.
G.f.: (1/x) * Product_{k>0} (1 + x^k) / (1 + x^(5*k))^5.
EXAMPLE
G.f. = 1/q + 1 + q + 2*q^2 + 2*q^3 - 2*q^4 - q^5 - 4*q^7 - 2*q^8 + 5*q^9 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (1/q) QPochhammer[ q^5, q^10]^5 / QPochhammer[ q, q^2], {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x*O(x^n); polcoeff( eta(x^2 + A) / eta(x + A) * (eta(x^5 + A) / eta(x^10 + A))^5, n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 07 2007
STATUS
approved