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))).

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

0,2

Links

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

G. E. Andrews, R. P. Lewis, J. Lovejoy, Partitions with designated summands, Acta Arith. 105 (2002), no. 1, 51-66.

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

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 *)

Crossrefs

Cf. A293426, A293629.

Cf. A102186 (PDO(n)).

Sequence in context: A329141 A090539 A262050 * A113478 A056601 A370943

Adjacent sequences: A293625 A293626 A293627 * A293629 A293630 A293631

Keyword

nonn

Author

Seiichi Manyama, Oct 13 2017

Status

approved