OFFSET
0,2
REFERENCES
O. Kolberg, The coefficients of j(tau) modulo powers of 3, Acta Univ. Bergen., Series Math., Arbok for Universitetet I Bergen, Mat.-Naturv. Serie, 1962 No. 16, pp. 1-7. See t, page 1.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..2500 from G. C. Greubel)
FORMULA
Expansion of (eta(q)^3 / eta(q^3))^2 in powers of q.
Euler transform of period 3 sequence [-6, -6, -4, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (9 t)) = 243 (t/i)^2 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A033686.
G.f.: Product_{k>0} ( (1 - x^k)^3 / (1 - x^(3*k)) )^2.
Convolution square of A005928.
EXAMPLE
G.f. = 1 - 6*q + 9*q^2 + 12*q^3 - 42*q^4 + 18*q^5 + 36*q^6 - 48*q^7 + 45*q^8 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ (QPochhammer[ q]^3 / QPochhammer[ q^3])^2, {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^3 / eta(x^3 + A))^2, n))};
(Sage) A = ModularForms( Gamma0(9), 2, prec=53) . basis(); A[0] - 6*A[1] + 9*A[2];
(Magma) A := Basis( ModularForms( Gamma0(9), 2), 53); A[1] - 6*A[2] + 9*A[3]; /* Michael Somos, Sep 27 2016 */
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, May 26 2014
STATUS
approved