A198958 q-expansion of modular form psi_0^6/t_{3B}^2.

0, 0, 1, 6, 27, 80, 207, 432, 863, 1512, 2646, 4144, 6585, 9504, 14216, 19476, 27783, 36384, 49977, 63504, 84722, 104736, 136188, 165056, 210717, 250560, 314270, 367902, 455544, 525808, 642762, 733968, 888087, 1003608, 1201554, 1347232

Offset: 0

Author

N. J. A. Sloane, Nov 01 2011

Keywords

• nonn

Comments

psi_0 is given in A004016, t_{3B} in A198955.

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

Examples

			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 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Masao Koike, Modular forms on non-compact arithmetic triangle groups, Unpublished manuscript [Extensively annotated with OEIS A-numbers by N. J. A. Sloane, Feb 14 2021.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.]

Crossrefs

Cf. A106402.

Programs

Magma

A := Basis( ModularForms( Gamma1(3), 6), 36); A[3]; /* Michael Somos, Feb 22 2015 */

Mathematica

a[ n_] := SeriesCoefficient[ q^2 (QPochhammer[ q^3]^3 / QPochhammer[ q])^6, {q, 0, n}]; (* Michael Somos, Feb 22 2015 *)

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 */

Formula

Expansion of (c(q) / 3)^6 in powers of q where c() is a cubic AGM theta function. - Michael Somos, Jun 07 2012

Expansion of (eta(q^3)^3 / eta(q))^6 in powers of q.

G.f.: (Product_{k>0} (1 - x^(3*k))^3 / (1 - x^k))^6. - Michael Somos, Jun 07 2012

Convolution square of A106402. - Michael Somos, Dec 26 2015