OFFSET
0,15
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
Euler transform of period 30 sequence [ 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -2, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, ...].
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = v^2 + u*(2 - 4*v + u*v).
G.f.: Product_{k>0} (1 + x^k) * (1 + x^(15*k)) / ((1 + x^(3*k)) * (1 + x^(5*k)))^2.
EXAMPLE
G.f. = 1 + q + q^2 - q^5 - q^6 + q^8 - q^10 + q^13 + 2*q^14 + q^15 - 2*q^16 - ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (QPochhammer[ q^3, q^6] QPochhammer[ q^5, q^10])^2 / (QPochhammer[ q, q^2] QPochhammer[ q^15, q^30]), {q, 0, n}]; (* Michael Somos, Apr 26 2015 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^30 + A) / (eta(x + A) * eta(x^15 + A)) * (eta(x^3 + A) * eta(x^5 + A) / (eta(x^6 + A) * eta(x^10 + A)))^2, n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Jul 16 2006
STATUS
approved