A257469 Expansion of f(-x) * psi(x^6) in powers of x where psi(), f() are Ramanujan theta functions.

1, -1, -1, 0, 0, 1, 1, 0, -1, 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, -1, -1, -1, 1, 1, 0, 1, 1, 0, 1, 0, -1, 0, 1, -1, 0, -1, 1, -1, -1, 0, 0, 0, 0, 1, 1, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 1, -1, 0, 1, 0, 1, 0, 1, 0, 1, -1, -1, -1, 0, 0, 0, -2, -1, 0

Offset

0,58

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 q^(-19/24) * eta(q) * eta(q^12)^2 / eta(q^6) in powers of q.

Euler transform of period 12 sequence [ -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -2, ...].

-2 * a(n) = A246962(3*n + 2).

Example

G.f. = 1 - x - x^2 + x^5 + x^6 - x^8 + x^11 - x^12 + x^13 - x^15 - x^19 + ...
G.f. = q^19 - q^43 - q^67 + q^139 + q^163 - q^211 + q^283 - q^307 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x] EllipticTheta[ 2, 0, x^3] / (2 x^(3/4)), {x, 0 , n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^12 + A)^2 / eta(x^6 + A), n))};

Crossrefs

Cf. A246962.

Sequence in context: A213185 A285716 A101606 * A275947 A337976 A125005

Adjacent sequences: A257466 A257467 A257468 * A257470 A257471 A257472

Keyword

sign

Author

Michael Somos, Apr 25 2015

Status

approved