A181977 Expansion of b(q) * c(q^3)^2 / 9 in powers of q where b(), c() are cubic AGM theta functions.

1, -3, 0, 8, -9, 0, 17, -27, 0, 40, -39, 0, 50, -72, 0, 96, -81, 0, 104, -150, 0, 176, -153, 0, 170, -243, 0, 280, -216, 0, 273, -360, 0, 400, -351, 0, 362, -510, 0, 560, -450, 0, 520, -648, 0, 736, -615, 0, 601, -864, 0, 936, -729, 0, 850, -1086, 0, 1160

Offset: 2

Author

Michael Somos, Apr 04 2012

Keywords

• sign

Comments

Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).

Examples

			G.f. = q^2 - 3*q^3 + 8*q^5 - 9*q^6 + 17*q^8 - 27*q^9 + 40*q^11 - 39*q^12 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 2..2500

Crossrefs

Cf. A106402.

Programs

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[(eta[q]* eta[q^9]^2/eta[q^3])^3, {q, 0, 50}], q] (* G. C. Greubel, Aug 11 2018 *)

PARI

{a(n) = my(A); if( n<2, 0, n = n-2; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^9 + A)^2 / eta(x^3 + A))^3, n))};

Formula

Expansion of (eta(q) * eta(q^9)^2 / eta(q^3))^3 in powers of q.

Euler transform of period 9 sequence [-3, -3, 0, -3, -3, 0, -3, -3, -6, ...].

a(3*n + 1) = 0. a(3*n) = -3 * A106402(n).