OFFSET
0,3
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^(-5/12) * eta(q^2)^5 * eta(q^12)^2 / (eta(q) * eta(q^4)^2 * eta(q^3)^3 * eta(q^6)) in powers of q.
Euler transform of period 12 sequence [ 1, -4, 4, -2, 1, 0, 1, -2, 4, -4, 1, 0, ...].
a(n) = A182032(12*n + 5).
EXAMPLE
G.f. = 1 + x - 3*x^2 + x^3 + 5*x^4 - 10*x^5 + 4*x^6 + 17*x^7 - 31*x^8 + ...
G.f. = q^5 + q^17 - 3*q^29 + q^41 + 5*q^53 - 10*q^65 + 4*q^77 + 17*q^89 + ...
MATHEMATICA
eta[x_] := x^(1/24)*QPochhammer[x]; A233037[n_] := SeriesCoefficient[q^(-5/12)*eta[q^2]^5* eta[q^12]^2/(eta[q]*eta[q^4]^2*eta[q^3]^3*eta[q^6]), {q, 0, n}];
Table[A233037[n], {n, 0, 50}] (* G. C. Greubel, Aug 10 2017 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^12 + A)^2 / (eta(x + A) * eta(x^4 + A)^2 * eta(x^3 + A)^3 * eta(x^6 + A)), n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Dec 03 2013
STATUS
approved