A255318 Expansion of psi(x^3) * f(x^2, x^4) in powers of x where psi(), f() are Ramanujan theta functions.

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

Offset

0,14

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 f(x^3) * f(-x^6) / chi(-x^2) in powers of x where chi(), f() are Ramanujan theta functions.

Expansion of q^(-11/24) * eta(q^4) * eta(q^6)^4 / (eta(q^2) * eta(q^3) * eta(q^12)) in powers of q.

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

Example

G.f. = 1 + x^2 + x^3 + x^4 + x^5 + x^7 + x^9 + x^10 + x^11 + 2*x^13 + ...
G.f. = q^11 + q^59 + q^83 + q^107 + q^131 + q^179 + q^227 + q^251 + q^275 + ...

Mathematica

a[ n_] := SeriesCoefficient[QPochhammer[-x^3]*QPochhammer[x^6]* QPochhammer[ -x^2, x^2], {x, 0, n}];

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A) * eta(x^6 + A)^4 / (eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)), n))};

Crossrefs

Sequence in context: A348040 A082858 A363164 * A249223 A115953 A225245

Adjacent sequences: A255315 A255316 A255317 * A255319 A255320 A255321

Keyword

nonn

Author

Michael Somos, Feb 21 2015

Status

approved