A244465 Expansion of f(-x^3, -x^5) in powers of x where f() is Ramanujan's two-variable theta function.

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

Offset: 0

Author

Michael Somos, Jun 28 2014

Keywords

• sign

Examples

			G.f. = 1 - x^3 - x^5 + x^14 + x^18 - x^33 - x^39 + x^60 + x^68 - x^95 + ...
G.f. = q - q^49 - q^81 + q^225 + q^289 - q^529 - q^625 + q^961 + q^1089 + ...
		

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

Crossrefs

Cf. A214264.

Programs

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ x^3, x^8] QPochhammer[ x^5, x^8] QPochhammer[ x^8], {x, 0, n}];

PARI

{a(n) = issquare( 16*n + 1) * (-1)^n};

Formula

Euler transform of period 8 sequence [ 0, 0, -1, 0, -1, 0, 0, -1, ...].

G.f.: f(-x^3, -x^5) = Sum_{k in Z} (-1)^k * x^(4*k^2 - k).

a(n) = (-1)^n * A214264(n).