OFFSET
0,4
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^(-2/3) * eta(q^2)^4 * eta(q^6)^2 * eta(q^12)^3 / (eta(q) * eta(q^3) * eta(q^4)^3) in powers of q.
Euler transform of period 12 sequence [ 1, -3, 2, 0, 1, -4, 1, 0, 2, -3, 1, -4, ...].
a(4*n) = 0. 24 * a(n) = A207541(3*n + 2).
EXAMPLE
x + x^2 - 2*x^3 + 3*x^5 - 2*x^6 - 4*x^7 + 5*x^9 + x^10 - 8*x^11 + ...
q^5 + q^8 - 2*q^11 + 3*q^17 - 2*q^20 - 4*q^23 + 5*q^29 + q^32 - 8*q^35 + ...
MATHEMATICA
a[n_]:=SeriesCoefficient[((QP[q^2]^4*QP[q^6]^2*QP[q^12]^3)/(QP[q]*QP[q^3]*
QP[q^4]^3)), {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Dec 17 2017 *)
PROG
(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^6 + A)^2 * eta(x^12 + A)^3 / (eta(x + A) * eta(x^3 + A) * eta(x^4 + A)^3), n))}
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Feb 26 2012
STATUS
approved