A244366 Expansion of c(q) * c(q^5) / 9 in powers of q where c() is a cubic AGM theta function.

1, 1, 2, 0, 2, 2, 3, 2, 1, 4, 5, 4, 6, 1, 8, 4, 7, 4, 2, 6, 8, 6, 12, 0, 10, 7, 14, 8, 2, 8, 17, 8, 14, 2, 16, 12, 16, 10, 3, 8, 18, 10, 20, 2, 18, 10, 23, 16, 1, 14, 24, 16, 20, 4, 30, 16, 22, 16, 5, 16, 24, 18, 30, 4, 28, 14, 32, 18, 6, 20, 33, 16, 26, 1

Offset

2,3

Comments

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

Links

Table of n, a(n) for n=2..75.

Formula

Expansion of (eta(q^3) * eta(q^15))^3 / (eta(q) * eta(q^5)) in powers of q.

Euler transform of period 15 sequence [ 1, 1, -2, 1, 2, -2, 1, 1, -2, 2, 1, -2, 1, 1, -4, ...].

a(5*n) = a(n) for all n in Z.

Given g.f. A = A0 + A1 + A2 + A3 + A4 is the 5-section, then 0 = A4*A3^2 - A4^2*A2 + A2^2*A1 - A3*A1^2 - 6*A3*A2*A0 + 6*A4*A1*A0.

Example

G.f. = q^2 + q^3 + 2*q^4 + 2*q^6 + 2*q^7 + 3*q^8 + 2*q^9 + q^10 + 4*q^11 + 5*q^12 + ...

Prog

(PARI) {a(n) = my(A); if( n<2, 0, n -= 2; A = x * O(x^n); polcoeff( (eta(x^3 + A) * eta(x^15 + A))^3 / (eta(x + A) * eta(x^5 + A)), n))};
(Magma) A := Basis( ModularForms( Gamma0(15), 2), 61); A[3] + A[4];

Crossrefs

Sequence in context: A159632 A164733 A288311 * A262676 A070101 A022830

Adjacent sequences: A244363 A244364 A244365 * A244367 A244368 A244369

Keyword

nonn

Author

Michael Somos, Nov 11 2014

Status

approved