OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(-15/24) * eta(q)^2 * eta(q^6)^6 / (eta(q^2)^3 * eta(q^3)^3 * eta(q^4)^2) in powers of q.
Euler transform of period 12 sequence [-2, 1, 1, 3, -2, -2, -2, 3, 1, 1, -2, 0, ...].
EXAMPLE
G.f. = 1 - 2*x + 2*x^2 - x^3 + 3*x^4 - 8*x^5 + 9*x^6 - 7*x^7 + ...
G.f. = q^5 - 2*q^13 + 2*q^21 - q^29 + 3*q^37 - 8*q^45 + 9*q^53 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ x^(-5/8) EllipticTheta[ 2 , 0, x^(3/2)]^3 / (EllipticTheta[ 2 , 0, x^(1/2)]^2 EllipticTheta[ 2 , 0, x]), {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^6 + A)^6 / (eta(x^2 + A)^3 * eta(x^3 + A)^3 * eta(x^4 + A)^2), n))};
(PARI) q='q+O('q^99); Vec(eta(q)^2*eta(q^6)^6/(eta(q^2)^3*eta(q^3)^3*eta(q^4)^2)) \\ Altug Alkan, Jul 31 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Sep 13 2015
STATUS
approved