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A226861
Expansion of phi(x) * f(-x^3) in powers of x where phi(), f() are Ramanujan theta functions.
2
1, 2, 0, -1, 0, 0, -1, -4, 0, 2, -2, 0, -2, 0, 0, -1, 4, 0, 0, 0, 0, 1, 0, 0, 2, 4, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, -2, 0, 0, -3, 0, 0, 0, 0, 0, 2, -4, 0, -2, -2, 0, 2, 0, 0, 0, -4, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 1, 4, 0, 0
OFFSET
0,2
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^(-1/8) * eta(q^2)^5 * eta(q^3) / (eta(q) * eta(q^4))^2 in powers of q.
Euler transform of period 12 sequence [2, -3, 1, -1, 2, -4, 2, -1, 1, -3, 2, -2, ...].
G.f.: (Sum_{k in Z} x^(k^2)) * Product_{k>0} (1 - x^(3*k)).
a(3*n + 2) = 0. a(3*n) = A226289(n).
EXAMPLE
G.f. = 1 + 2*x - x^3 - x^6 - 4*x^7 + 2*x^9 - 2*x^10 - 2*x^12 - x^15 + 4*x^16 + ...
G.f. = q + 2*q^9 - q^25 - q^49 - 4*q^57 + 2*q^73 - 2*q^81 - 2*q^97 - q^121 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q] QPochhammer[ q^3], {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^3 + A) / (eta(x + A) * eta(x^4 + A))^2, n))};
CROSSREFS
Cf. A226289.
Sequence in context: A286604 A366784 A217540 * A185643 A363051 A278515
KEYWORD
sign
AUTHOR
Michael Somos, Jun 20 2013
STATUS
approved