A182035 Expansion of chi(-q) * chi(-q^2) * chi(-q^6) * psi(q^6)^2 / (psi(q^9) * phi(-q^9)) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.

1, -1, -1, 0, 1, 0, 0, 0, 1, 0, -2, 0, 0, 2, 0, 0, 1, 0, 0, -4, -2, 0, 4, 0, 0, 1, 2, 0, -8, 0, 0, 8, 1, 0, 2, 0, 0, -14, -4, 0, 14, 0, 0, 4, 4, 0, -24, 0, 0, 23, 1, 0, 6, 0, 0, -40, -8, 0, 38, 0, 0, 10, 8, 0, -63, 0, 0, 60, 2, 0, 16, 0, 0, -98, -14, 0, 92

Offset: 0

Author

Michael Somos, Apr 07 2012

Keywords

• sign

Comments

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

Examples

			1 - q - q^2 + q^4 + q^8 - 2*q^10 + 2*q^13 + q^16 - 4*q^19 - 2*q^20 + ...
		

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. A092848

Programs

Mathematica

eta[x_] := x^(1/24)*QPochhammer[x]; A182035[n_] := SeriesCoefficient[ eta[q]*eta[q^12]^3/(eta[q^4]*eta[q^6]*eta[q^9]*eta[q^18] ), {q, 0, n}];
Table[A182035[n], {n,0,50}] (* G. C. Greubel, Aug 21 2017 *)

PARI

{a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^12 + A)^3 / (eta(x^4 + A) * eta(x^6 + A) * eta(x^9 + A) * eta(x^18 + A)), n))}

Formula

Expansion of eta(q) * eta(q^12)^3 / (eta(q^4) * eta(q^6) * eta(q^9) * eta(q^18)) in powers of q.

Euler transform of period 36 sequence [ -1, -1, -1, 0, -1, 0, -1, 0, 0, -1, -1, -2, -1, -1, -1, 0, -1, 2, -1, 0, -1, -1, -1, -2, -1, -1, 0, 0, -1, 0, -1, 0, -1, -1, -1, 0, ...].

a(3*n) = 0 unless n=0. a(3*n + 1) = a(6*n + 2) = -A092848(n).