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.

A293426 Expansion of Product_{k>0} ((1 - q^(3*k))^3*(1 - q^(6*k))^3)/((1 - q^k)^5*(1 - q^(2*k))^3).

Original entry on oeis.org

1, 5, 23, 77, 244, 677, 1794, 4411, 10454, 23597, 51699, 109378, 225804, 453893, 893872, 1723286, 3265023, 6078557, 11148496, 20146561, 35935772, 63287458, 110186562, 189715530, 323335946, 545666040, 912512366, 1512613763, 2486819428, 4056167621, 6566647376
Offset: 0

Views

Author

Seiichi Manyama, Oct 09 2017

Keywords

Crossrefs

Cf. A077285 (PD(n)).

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Product[((1 - x^(3*k))^3 * (1 - x^(6*k))^3) / ((1 - x^k)^5 * (1 - x^(2*k))^3), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 09 2017 *)
    max = 30; QP = QPochhammer; s = QP[q^6]/(QP[q]*QP[q^2]*QP[q^3]) + O[q]^(3 max + 3); (1/3)*Table[CoefficientList[s, q][[3*n + 3]], {n, 0, max}] (* Jean-François Alcover, Oct 10 2017, from 1st formula *)
  • PARI
    m = 40; Vec(prod(k=1, m, ((1 - q^(3*k))^3*(1 - q^(6*k))^3)/((1 - q^k)^5*(1 - q^(2*k))^3)) + O(q^m)) \\ Michel Marcus, Oct 10 2017

Formula

a(n) = (1/3) * A077285(3*n+2).
a(n) ~ 5^(3/4) * exp(sqrt(10*n/3)*Pi) / (2^(11/4) * 3^(15/4) * n^(5/4)). - Vaclav Kotesovec, Oct 09 2017