A281743 Expansion of chi(-x) * chi(-x^4) / (chi(-x^3) * chi(-x^12)) in powers of x where chi() is a Ramanujan theta function.

1, -1, 0, 0, -1, 0, 1, -1, 1, 1, -1, 0, 1, -2, 1, 1, -1, 0, 2, -3, 0, 2, -2, 0, 4, -4, 1, 3, -5, 0, 5, -6, 3, 4, -6, 0, 6, -9, 3, 6, -7, 1, 9, -12, 2, 9, -11, 1, 15, -17, 4, 12, -18, 2, 19, -23, 8, 17, -23, 3, 22, -31, 9, 23, -28, 3, 31, -41, 8, 31, -39, 5, 46

Offset

0,14

Comments

The sequence generating function appears on the right side of one of Ramanujan's Forty identities.

Rogers-Ramanujan functions: G(q) (see A003114), H(q) (A003106).

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 G(x^8) * H(x^3) - x * G(x^3) * H(x^8) in powers of x where G(), H() are Rogers-Ramanujan functions.

Expansion of q^(-5/12) * eta(q) * eta(q^4) * eta(q^6) * eta(q^24) / (eta(q^2) * eta(q^3) * eta(q^8) * eta(q^12)) in powers of q.

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

Example

G.f. = 1 - x - x^4 + x^6 - x^7 + x^8 + x^9 - x^10 + x^12 - 2*x^13 + ...
G.f. = q^5 - q^17 - q^53 + q^77 - q^89 + q^101 + q^113 - q^125 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x, x^2] QPochhammer[ x^4, x^8] QPochhammer[ -x^3, x^3] QPochhammer[ -x^12, x^12], {x, 0, n}];

Prog

(PARI) {a(n) = if( n<0, 0, my(A = x * O(x^n)); polcoeff( eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^24 + A) / (eta(x^2 + A) * eta(x^3 + A) * eta(x^8 + A) * eta(x^12 + A)), n))};

Crossrefs

Sequence in context: A064272 A117479 A200650 * A118404 A089339 A249303

Adjacent sequences: A281740 A281741 A281742 * A281744 A281745 A281746

Keyword

sign

Author

Michael Somos, Jan 28 2017

Status

approved