OFFSET
-1,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of (1/q) * chi(-q)^2 * chi(-q^4) * chi(q^3)^2 * chi(-q^12) in powers of q where chi() is a Ramanujan theta function.
Expansion of eta(q)^2 * eta(q^4) * eta(q^6)^4 / (eta(q^2)^2 * eta(q^3)^2 * eta(q^8) * eta(q^12) * eta(q^24)) in powers of q.
Euler transform of period 24 sequence [ -2, 0, 0, -1, -2, -2, -2, 0, 0, 0, -2, -2, -2, 0, 0, 0, -2, -2, -2, -1, 0, 0, -2, 0, ...].
EXAMPLE
G.f. = 1/q - 2 + q - q^3 + q^5 + 2*q^7 - q^9 - 2*q^11 - q^13 + 3*q^15 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (1/q) QPochhammer[ q, q^2]^2 QPochhammer[ q^4, q^8] QPochhammer[ -q^3, q^6]^2 QPochhammer[ q^12, q^24], {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^4 + A) * eta(x^6 + A)^4 / (eta(x^2 + A)^2 * eta(x^3 + A)^2 * eta(x^8 + A) * eta(x^12 + A) * eta(x^24 + A)), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Feb 22 2015
STATUS
approved