OFFSET
2,3
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
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 11 2014
STATUS
approved