%I #31 Sep 08 2022 08:46:00
%S 0,0,1,6,27,80,207,432,863,1512,2646,4144,6585,9504,14216,19476,27783,
%T 36384,49977,63504,84722,104736,136188,165056,210717,250560,314270,
%U 367902,455544,525808,642762,733968,888087,1003608,1201554,1347232
%N q-expansion of modular form psi_0^6/t_{3B}^2.
%C psi_0 is given in A004016, t_{3B} in A198955.
%C Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).
%H G. C. Greubel, <a href="/A198958/b198958.txt">Table of n, a(n) for n = 0..1000</a>
%H Masao Koike, <a href="https://oeis.org/A004016/a004016.pdf">Modular forms on non-compact arithmetic triangle groups</a>, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021. I wrote 2005 on the first page but the internal evidence suggests 1997.]
%F Expansion of (c(q) / 3)^6 in powers of q where c() is a cubic AGM theta function. - _Michael Somos_, Jun 07 2012
%F Expansion of (eta(q^3)^3 / eta(q))^6 in powers of q.
%F G.f.: (Product_{k>0} (1 - x^(3*k))^3 / (1 - x^k))^6. - _Michael Somos_, Jun 07 2012
%F Convolution square of A106402. - _Michael Somos_, Dec 26 2015
%e G.f. = q^2 + 6*q^3 + 27*q^4 + 80*q^5 + 207*q^6 + 432*q^7 + 863*q^8 + 1512*q^9 + ...
%t a[ n_] := SeriesCoefficient[ q^2 (QPochhammer[ q^3]^3 / QPochhammer[ q])^6, {q, 0, n}]; (* _Michael Somos_, Feb 22 2015 *)
%o (PARI) {a(n) = my(A); if( n<2, 0, n -= 2; A = x * O(x^n); polcoeff( (eta(x^3 + A)^3 / eta(x + A))^6, n))}; /* _Michael Somos_, Jun 07 2012 */
%o (Magma) A := Basis( ModularForms( Gamma1(3), 6), 36); A[3]; /* _Michael Somos_, Feb 22 2015 */
%Y Cf. A106402.
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Nov 01 2011