A262967 - OEIS

A262967

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, -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

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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..2500

Michael Somos, Introduction to Ramanujan theta functions

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

Adjacent sequences: A262964 A262965 A262966 * A262968 A262969 A262970

KEYWORD

sign

AUTHOR

Michael Somos, Oct 05 2015

STATUS

approved