A279255 Expansion of chi(x) * chi(-x^3) * chi(-x^8) * chi(-x^24) in powers of x where chi() is a Ramanujan theta function.

1, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, -3, 0, 0, 0, -1, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, -1, -5, 0, 0, 0, -2, 0, 0, 0, 5, 0

Offset: 0

Author

Michael Somos, Dec 08 2016

Keywords

• sign

Comments

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

Examples

			G.f. = 1 + x + x^5 - x^9 + x^12 + x^17 - x^24 - x^25 - x^29 + 2*x^33 + ...
G.f. = q^-3 + q^-1 + q^7 - q^15 + q^21 + q^31 - q^45 - q^47 - q^55 + ...
		

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. A029838.

Programs

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^2] QPochhammer[ x^3, x^6] QPochhammer[ x^8, x^16] QPochhammer[ x^24, x^48], {x, 0, n}];

PARI

{a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A) * eta(x^8 + A) * eta(x^24 + A) / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^16 + A) * eta(x^48 + A)), n))};

Formula

Euler transform of period 48 sequence [ 1, -1, 0, 0, 1, -1, 1, -1, 0, -1, 1, 0, 1, -1, 0, 0, 1, -1, 1, 0, 0, -1, 1, -2, 1, -1, 0, 0, 1, -1, 1, 0, 0, -1, 1, 0, 1, -1, 0, -1, 1, -1, 1, 0, 0, -1, 1, 0, ...].

a(4*n + 2) = a(4*n + 3) = a(6*n + 2) = a(6*n + 4) = 0.

a(4*n + 1) = a(12*n) = A029838(n).