A258092 Expansion of f(x, x^2) / psi(x)^3 in powers of x where psi(), f(, ) are Ramanujan theta functions.

1, -2, 4, -10, 20, -36, 64, -112, 189, -308, 492, -778, 1210, -1844, 2776, -4144, 6114, -8914, 12884, -18484, 26302, -37124, 52040, -72512, 100415, -138196, 189160, -257648, 349184, -470932, 632312, -845472, 1125853, -1493222, 1973060, -2597892, 3408754

Offset

0,2

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^(1/3) * eta(q)^2 * eta(q^3)^2 / (eta(q^2)^5 * eta(q^6)) in powers of q.

Euler transform of period 6 sequence [-2, 3, -4, 3, -2, 2, ...].

G.f.: Product_{k>0} (1 - x^(3*k)) / ((1 + x^(3*k)) * (1 + x^k)^2 * (1 - x^(2*k))^3).

a(n) = A258093(3*n - 1).

Example

G.f. = 1 - 2*x + 4*x^2 - 10*x^3 + 20*x^4 - 36*x^5 + 64*x^6 - 112*x^7 + ...
G.f. = 1/q - 2*q^2 + 4*q^5 - 10*q^8 + 20*q^11 - 36*q^14 + 64*q^17 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x]^2 QPochhammer[ x^3]^2 / ( QPochhammer[ x^2]^5 QPochhammer[ x^6]), {x, 0, n}]; (* Michael Somos, May 25 2015 *)

Prog

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

Crossrefs

Cf. A258093.

Sequence in context: A174175 A127392 A236001 * A263993 A189585 A239346

Adjacent sequences: A258089 A258090 A258091 * A258093 A258094 A258095

Keyword

sign

Author

Michael Somos, May 19 2015

Status

approved