A293423 Expansion of Product_{k>0} (1 - q^(3*k))^5/((1 - q^k)^3*(1 - q^(6*k))^2).

1, 3, 9, 17, 36, 63, 118, 195, 333, 528, 852, 1305, 2020, 3012, 4518, 6583, 9624, 13761, 19698, 27702, 38952, 54000, 74784, 102357, 139882, 189297, 255690, 342497, 457824, 607617, 804656, 1058970, 1390545, 1815984, 2366268, 3068388, 3970008, 5114382, 6574266

Offset: 0

Author

Seiichi Manyama, Oct 08 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A293421.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i>1, b(n, i-1), 0)+
      add((p-> p+[0, p[1]])(b(n-i*j, min(n-i*j, i-1))*j), j=`if`(i=1, n, 1..n/i)))
    end:
a:= n-> (p-> 2*p[2]+p[1])(b(n$2)):
seq(a(n), n=0..38);  # Alois P. Heinz, Jul 18 2025

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 - x^(3*k))^5 / ((1 - x^k)^3 * (1 - x^(6*k))^2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 09 2017 *)

Formula

a(n) ~ 5^(1/4) * exp(sqrt(10*n)*Pi/3) / (9*2^(1/4)*n^(3/4)). - Vaclav Kotesovec, Oct 09 2017