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A262968
Expansion of phi(-q^6) / phi(-q) in powers of q where phi() is a Ramanujan theta function.
2
1, 2, 4, 8, 14, 24, 38, 60, 92, 138, 204, 296, 424, 600, 840, 1164, 1598, 2176, 2940, 3944, 5256, 6960, 9164, 12000, 15634, 20270, 26160, 33616, 43020, 54840, 69648, 88140, 111164, 139748, 175136, 218832, 272646, 338760, 419792, 518880, 639780, 786976, 965820
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 eta(q^2) * eta(q^6)^2 / (eta(q)^2 * eta(q^12)) in powers of q.
Euler transform of period 12 sequence [ 2, 1, 2, 1, 2, -1, 2, 1, 2, 1, 2, 0, ...].
a(n) = A262967(3*n).
a(n) ~ 5^(1/4) * exp(sqrt(5*n/6)*Pi) / (2^(9/4) * 3^(3/4) * n^(3/4)). - Vaclav Kotesovec, Oct 06 2015
EXAMPLE
G.f. = 1 + 2*q + 4*q^2 + 8*q^3 + 14*q^4 + 24*q^5 + 38*q^6 + 60*q^7 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q^6] / EllipticTheta[ 4, 0, q], {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^6 + A)^2 / (eta(x + A)^2 * eta(x^12 + A)), n))};
CROSSREFS
Cf. A262967.
Sequence in context: A290845 A100250 A053800 * A261203 A281968 A091774
KEYWORD
nonn
AUTHOR
Michael Somos, Oct 05 2015
STATUS
approved