A257400 - OEIS

A257400

Expansion of psi(q) * phi(q^2) * chi(-q^3) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.

1, 1, 2, 2, -1, 0, -2, 0, 2, 0, 0, -4, -2, 0, 0, 0, -1, -4, 0, 2, 0, 0, -2, 0, -2, 1, 0, -2, 0, 0, 0, 0, 2, 4, -2, 0, 0, 0, 4, 0, 0, -4, 0, 2, 4, 0, 0, 0, -2, 1, 2, 4, 0, 0, 2, 0, 0, 4, 0, -4, 0, 0, 0, 0, -1, 0, -4, 2, 4, 0, 0, 0, 0, 2, 0, 2, -2, 0, 0, 0, 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^3) * eta(q^4)^5 / (eta(q) * eta(q^8)^2 * eta(q^6)) in powers of q.

Euler transform of period 24 sequence [1, 1, 0, -4, 1, 1, 1, -2, 0, 1, 1, -4, 1, 1, 0, -2, 1, 1, 1, -4, 0, 1, 1, -2, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (144 t)) = 2592^(1/2) (t/i) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A257399.

a(8*n + 7) = 0.

EXAMPLE

G.f. = 1 + q + 2*q^2 + 2*q^3 - q^4 - 2*q^6 + 2*q^8 - 4*q^11 - 2*q^12 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, q^(1/2)] EllipticTheta[ 3, 0, q^2] QPochhammer[ q^3, q^6] / (2 q^(1/8)), {q, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^3 + A) * eta(x^4 + A)^5 / (eta(x + A) * eta(x^8 + A)^2 * eta(x^6 + A)), n))};

CROSSREFS

Cf. A257399.

Sequence in context: A332813 A323077 A334201 * A328081 A194853 A309866

Adjacent sequences: A257397 A257398 A257399 * A257401 A257402 A257403

KEYWORD

sign

AUTHOR

Michael Somos, Apr 21 2015

STATUS

approved