A257402 Expansion of chi(x) * psi(-x^3) * psi(x^12) in powers of x where psi(), chi() are Ramanujan theta functions.

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

Offset: 0

Author

Michael Somos, Apr 21 2015

Keywords

• nonn

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^8 + x^12 + x^13 + x^16 + x^17 + x^20 + x^21 + x^28 + ...
G.f. = q^11 + q^17 + q^41 + q^59 + q^83 + q^89 + q^107 + q^113 + q^131 + ...
		

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. A255318, A255319.

Programs

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^2] EllipticTheta[ 2, 0, x^6] EllipticTheta[ 2, Pi/4, x^(3/2)] / (2^(3/2) x^(15/8)), {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^24 + A)^2 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A)), n))};

Formula

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

a(4*n) = A255318(n). a(4*n + 1) = A255319(n). a(4*n + 2) = a(4*n + 3) = 0.