A304885 Expansion of Product_{k>=1} 1/(1-x^(3*k-2)) * Product_{k>=1} 1/(1-x^(6*k-1)).

1, 1, 1, 1, 2, 3, 3, 4, 5, 6, 8, 10, 12, 14, 17, 21, 25, 30, 35, 41, 49, 58, 68, 79, 92, 107, 124, 144, 166, 191, 220, 252, 289, 331, 378, 431, 490, 557, 632, 717, 812, 917, 1035, 1167, 1315, 1480, 1663, 1866, 2092, 2344, 2624, 2934, 3277, 3656, 4076, 4542, 5056

Offset: 0

Author

Seiichi Manyama, May 20 2018

Keywords

• nonn

Links

• Sylvie Corteel, Carla D. Savage, and Andrew V. Sills. F. Beukers, Lecture hall sequences, q-series, and asymmetric partition identities, In Alladi K., Garvan F. (eds) Partitions, q-Series, and Modular Forms pp 53-68. Developments in Mathematics, vol 23. Springer, New York, NY.

Crossrefs

Cf. A035382, A109702, A304883.

Programs

Maple

seq(coeff(series(mul(1/(1-x^(3*k-2)),k=1..n)*mul(1/(1-x^(6*k-1)),k=1..n), x,70),x,n),n=0..60); # Muniru A Asiru, May 21 2018

Mathematica

nmax = 50; CoefficientList[Series[Product[1/((1-x^(3*k-2)) * (1-x^(6*k-1))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 21 2018 *)

Formula

G.f.: Sum_{j>=0} x^(j*(3*j-1)/2)*(Product_{k=1..j} (1-x^(6*k-4)))/(Product_{k=1..3*j} (1-x^k)).

a(n) ~ exp(Pi*sqrt(n/3)) * Pi^(2/3) / (2 * 3^(2/3) * Gamma(1/3) * n^(5/6)). - Vaclav Kotesovec, May 21 2018