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 q^(-1/4) * (eta(q)^5 / eta(q^2))^2 in powers of q.
Expansion of phi(-x)^5 * f(-x^2)^3 = phi(-x)^2 * f(-x)^6 in powers of x where phi(), f() are Ramanujan theta functions.
Euler transform of period 2 sequence [ -10, -8, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (32 t)) = 8192 (t / i)^4 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A227317.
G.f.: (Product_{k>0} (1 - x^k)^5 / (1 - x^(2*k)))^2.
EXAMPLE
G.f. = 1 - 10*x + 37*x^2 - 50*x^3 - 30*x^4 + 128*x^5 - 25*x^6 - 34*x^7 - 320*x^8 + ...
G.f. = q - 10*q^5 + 37*q^9 - 50*q^13 - 30*q^17 + 128*q^21 - 25*q^25 - 34*q^29 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (QPochhammer[ x]^5 / QPochhammer[ x^2])^2, {x, 0, n}];
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^5 / eta(x^2 + A))^2, n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 02 2013
STATUS
approved