A293628 - OEIS

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))).

%I #14 Oct 15 2017 05:31:04

%S 1,4,11,28,64,136,274,528,982,1772,3115,5352,9012,14904,24252,38888,

%T 61527,96156,148584,227204,344056,516296,768206,1133952,1661326,

%U 2416816,3492442,5014932,7157996,10158672,14339032,20134888,28133641,39124028,54161282,74652260

%N 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))).

%H Seiichi Manyama, <a href="/A293628/b293628.txt">Table of n, a(n) for n = 0..10000</a>

%H G. E. Andrews, R. P. Lewis, J. Lovejoy, <a href="http://dx.doi.org/10.4064/aa105-1-5">Partitions with designated summands</a>, Acta Arith. 105 (2002), no. 1, 51-66.

%F a(n) = (1/2) * A102186(3*n+2).

%F 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

%t 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 *)

%Y Cf. A293426, A293629.

%Y Cf. A102186 (PDO(n)).

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 13 2017