cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A293628 Expansion of Product_{k>0} ((1 - q^(2*k))^3*(1 - q^(6*k))*(1 - q^(12*k)))/((1 - q^k)^4*(1 - q^(4*k))).

Original entry on oeis.org

1, 4, 11, 28, 64, 136, 274, 528, 982, 1772, 3115, 5352, 9012, 14904, 24252, 38888, 61527, 96156, 148584, 227204, 344056, 516296, 768206, 1133952, 1661326, 2416816, 3492442, 5014932, 7157996, 10158672, 14339032, 20134888, 28133641, 39124028, 54161282, 74652260
Offset: 0

Views

Author

Seiichi Manyama, Oct 13 2017

Keywords

Crossrefs

Cf. A102186 (PDO(n)).

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[Product[(1+x^k)^3 * (1-x^(6*k)) * (1-x^(12*k)) / ((1-x^k) * (1-x^(4*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 15 2017 *)

Formula

a(n) = (1/2) * A102186(3*n+2).
a(n) ~ 5^(1/4) * exp(sqrt(5*n/3)*Pi) / (2^(7/2) * 3^(5/4) * n^(3/4)). - Vaclav Kotesovec, Oct 15 2017