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A262967
Expansion of phi(-q^2) / phi(-q^3) in powers of q where phi() is a Ramanujan theta function.
3
1, 0, -2, 2, 0, -4, 4, 0, -6, 8, 0, -12, 14, 0, -20, 24, 0, -32, 38, 0, -52, 60, 0, -80, 92, 0, -120, 138, 0, -180, 204, 0, -262, 296, 0, -376, 424, 0, -536, 600, 0, -752, 840, 0, -1044, 1164, 0, -1440, 1598, 0, -1966, 2176, 0, -2660, 2940, 0, -3580, 3944, 0
OFFSET
0,3
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 eta(q^2)^2 * eta(q^6) / (eta(q^3)^2 * eta(q^4)) in powers of q.
Euler transform of period 12 sequence [0, -2, 2, -1, 0, -1, 0, -1, 2, -2, 0, 0, ...].
a(3*n + 1) = 0.
Convolution inverse of A262966.
EXAMPLE
G.f. = 1 - 2*q^2 + 2*q^3 - 4*q^5 + 4*q^6 - 6*q^8 + 8*q^9 - 12*q^11 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q^2] / EllipticTheta[ 4, 0, 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)^2 * eta(x^6 + A) / (eta(x^3 + A)^2 * eta(x^4 + A)), n))};
(PARI) q='q+O('q^99); Vec(eta(q^2)^2*eta(q^6)/(eta(q^3)^2*eta(q^4))) \\ Altug Alkan, Jul 31 2018
CROSSREFS
Cf. A262966.
Sequence in context: A217840 A181615 A141333 * A168090 A078029 A078030
KEYWORD
sign
AUTHOR
Michael Somos, Oct 05 2015
STATUS
approved