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^(-11/24) * eta(q^2)^2 * eta(q^3)^3 / eta(q)^2 in powers of q.
Euler transform of period 6 sequence [ 2, 0, -1, 0, 2, -3, ...].
6 * a(n) = A213618(24*n + 11).
EXAMPLE
G.f. = 1 + 2*x + 3*x^2 + 3*x^3 + 3*x^4 + 5*x^5 + 4*x^6 + 5*x^7 + 4*x^8 + 5*x^9 + ...
G.f. = q^11 + 2*q^35 + 3*q^59 + 3*q^83 + 3*q^107 + 5*q^131 + 4*q^155 + 5*q^179 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^2 QPochhammer[ x^3]^3 / QPochhammer[x]^2, {x, 0, n}]; (* Michael Somos, Apr 26 2015 *)
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 + A)^2, n))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jun 16 2012
STATUS
approved