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A261444
Expansion of f(x^3)^2 * f(-x^6)^2 / f(-x^2) in powers of x where f() is a Ramanujan theta function.
5
1, 0, 1, 2, 2, 2, 0, 4, 2, 0, 1, 4, 4, 2, 2, 4, 5, 0, 2, 2, 6, 4, 2, 4, 6, 0, 0, 6, 4, 2, 4, 8, 7, 0, 2, 10, 4, 6, 0, 4, 6, 0, 1, 6, 8, 6, 4, 8, 4, 0, 4, 8, 10, 4, 2, 8, 8, 0, 2, 6, 12, 4, 4, 8, 8, 0, 5, 8, 6, 4, 0, 8, 14, 0, 2, 10, 8, 10, 2, 8, 11, 0, 6, 6, 6
OFFSET
0,4
COMMENTS
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
LINKS
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(-2/3) * eta(q^6)^8 / (eta(q^2) * eta(q^3)^2 * eta(q^12)^2) in powers of q.
Euler transform of period 12 sequence [ 0, 1, 2, 1, 0, -5, 0, 1, 2, 1, 0, -3, ...].
a(n) = A261426(2*n + 1).
EXAMPLE
G.f. = 1 + x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 4*x^7 + 2*x^8 + x^10 + ...
G.f. = q^2 + q^8 + 2*q^11 + 2*q^14 + 2*q^17 + 4*q^23 + 2*q^26 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ -x^3]^2 QPochhammer[ x^6]^2 / QPochhammer[ x^2], {x, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^6 + A)^8 / (eta(x^2 + A) * eta(x^3 + A)^2 * eta(x^12 + A)^2), n))};
CROSSREFS
Cf. A261426.
Sequence in context: A091399 A350951 A263527 * A000091 A155123 A125938
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 18 2015
STATUS
approved