A262968 Expansion of phi(-q^6) / phi(-q) in powers of q where phi() is a Ramanujan theta function.

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

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 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

Adjacent sequences: A262965 A262966 A262967 * A262969 A262970 A262971

Keyword

nonn

Author

Michael Somos, Oct 05 2015

Status

approved