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^(-23/24) * eta(q^2)^2 * eta(q^3)^3 * eta(q^8)^2 / (eta(q)^2 * eta(q^4)) in powers of q.
Euler transform of period 24 sequence [ 2, 0, -1, 1, 2, -3, 2, -1, -1, 0, 2, -2, 2, 0, -1, -1, 2, -3, 2, 1, -1, 0, 2, -4, ...].
6 * a(n) = A260158(4*n + 3).
EXAMPLE
G.f. = 1 + 2*x + 3*x^2 + 3*x^3 + 4*x^4 + 7*x^5 + 7*x^6 + 8*x^7 + 7*x^8 + ...
G.f. = q^23 + 2*q^47 + 3*q^71 + 3*q^95 + 4*q^119 + 7*q^143 + 7*q^167 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (1/2) x^(-1/2) EllipticTheta[ 2, 0, x^2] QPochhammer[ x^3]^3 QPochhammer[ -x, x]^2, {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^8 + A)^2 / (eta(x + A)^2 * eta(x^4 + A)), n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 09 2015
STATUS
approved