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^(-5/8) * eta(q^2)^7 * eta(q^8)^2 / (eta(q)^3 * eta(q^4)^3) in powers of q.
Euler transform of period 8 sequence [3, -4, 3, -1, 3, -4, 3, -3, ...].
EXAMPLE
G.f. = 1 + 3*x + 2*x^2 + x^3 + 5*x^4 + 5*x^5 + 3*x^6 + 5*x^7 + 4*x^8 + ...
G.f. = q^5 + 3*q^13 + 2*q^21 + q^29 + 5*q^37 + 5*q^45 + 3*q^53 + 5*q^61 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(-5/8)* eta[q^2]^7*eta[q^8]^2/(eta[q]^3*eta[q^4]^3), {q, 0, 60}], q]]; Table[ a[[n]], {n, 1, 50}] (* G. C. Greubel, Aug 05 2018 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^7 * eta(x^8 + A)^2 / (eta(x + A)^3 * eta(x^4 + A)^3), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 04 2014
STATUS
approved