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A244366 Expansion of c(q) * c(q^5) / 9 in powers of q where c() is a cubic AGM theta function. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 11 15:46 EST 2019. Contains 329018 sequences. (Running on oeis4.)