A262056 Expansion of phi(q^2) / phi(-q^3) in powers of q where phi() is a Ramanujan theta function.

1, 0, 2, 2, 0, 4, 4, 0, 10, 8, 0, 20, 14, 0, 36, 24, 0, 64, 42, 0, 108, 68, 0, 176, 108, 0, 280, 170, 0, 436, 260, 0, 666, 392, 0, 1000, 584, 0, 1480, 856, 0, 2160, 1240, 0, 3116, 1780, 0, 4448, 2526, 0, 6286, 3552, 0, 8804, 4956, 0, 12228, 6856, 0, 16852

Offset

0,3

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^4)^5 * eta(q^6) / (eta(q^2)^2 * eta(q^3)^2 * eta(q^8)^2) in powers of q.

Euler transform of period 24 sequence [ 0, 2, 2, -3, 0, 3, 0, -1, 2, 2, 0, -2, 0, 2, 2, -1, 0, 3, 0, -3, 2, 2, 0, 0, ...].

a(n) = A143068(2*n). a(3*n + 1) = 0.

Example

G.f. = 1 + 2*q^2 + 2*q^3 + 4*q^5 + 4*q^6 + 10*q^8 + 8*q^9 + 20*q^11 + ...

Mathematica

a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 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^4 + A)^5 * eta(x^6 + A) / (eta(x^2 + A)^2 * eta(x^3 + A)^2 * eta(x^8 + A)^2), n))};

Crossrefs

Cf. A143068.

Sequence in context: A168090 A078029 A078030 * A264628 A241320 A073469

Adjacent sequences: A262053 A262054 A262055 * A262057 A262058 A262059

Keyword

nonn

Author

Michael Somos, Sep 09 2015

Status

approved