A255257 Expansion of psi(x) * phi(-x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions.

1, 1, -4, -3, 4, 0, 1, 4, 0, 4, -3, -4, -4, -8, 8, 1, -4, 0, 0, 4, 0, 5, 4, 8, -4, -4, 4, -8, -3, -4, 4, -4, 0, 0, -8, 4, 1, 0, -8, 0, 4, 8, 8, 8, 0, 1, 0, -8, 8, -4, -4, -8, 12, 4, -12, 1, -4, 0, 0, -4, -8, 4, -8, 0, 0, -8, 1, 12, 8, 8, 0, -8, 8, 0, 8, 4, 0

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 q^(-1/8) * eta(q^2)^6 / (eta(q) * eta(q4)^2) in powers of q.

Euler transform of period 4 sequence [ 1, -5, 1, -3, ...].

a(n) = A034950(4*n).

Example

G.f. = 1 + x - 4*x^2 - 3*x^3 + 4*x^4 + x^6 + 4*x^7 + 4*x^9 - 3*x^10 + ...
G.f. = q + q^9 - 4*q^17 - 3*q^25 + 4*q^33 + q^49 + 4*q^57 + 4*q^73 + ...

Mathematica

a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^2] ^2 EllipticTheta[ 2, 0, x^(1/2)] / (2 x^(1/8)), {x, 0, n}];

Prog

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

Crossrefs

Cf. A034950.

Sequence in context: A309046 A007568 A091884 * A306769 A336031 A329982

Adjacent sequences: A255254 A255255 A255256 * A255258 A255259 A255260

Keyword

sign

Author

Michael Somos, Feb 19 2015

Status

approved