A014970 Expansion of (theta_3 / theta_4)^3.

1, 12, 72, 304, 1056, 3240, 9056, 23520, 57600, 134332, 300528, 648720, 1357184, 2761800, 5482944, 10645664, 20256768, 37842264, 69511272, 125712624, 224104896, 394198912, 684799776, 1175834016, 1996991488

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.

Links

• Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 11.

Programs

Mathematica

nmax=60; CoefficientList[Series[Product[((1+x^(2*k+1))/(1-x^(2*k+1)))^6,{k,0,nmax}],{x,0,nmax}],x] (* Vaclav Kotesovec, Aug 28 2015 *)

Formula

a(n) ~ exp(Pi*sqrt(3*n)) * 3^(1/4) / (16 * sqrt(2) * n^(3/4)). - Vaclav Kotesovec, Aug 28 2015