A304883 Expansion of Product_{k>=1} 1/(1-x^(3*k-1)) * Product_{k>=1} 1/(1-x^(6*k-5)).

1, 1, 2, 2, 3, 4, 5, 7, 9, 11, 14, 17, 21, 26, 32, 39, 47, 56, 67, 80, 95, 113, 133, 156, 183, 214, 250, 291, 338, 391, 452, 521, 600, 690, 791, 906, 1035, 1181, 1346, 1532, 1741, 1975, 2238, 2532, 2862, 3231, 3643, 4103, 4615, 5186, 5822, 6529, 7315, 8187, 9154

Offset

0,3

Links

Table of n, a(n) for n=0..54.

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.

Formula

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

a(n) ~ exp(Pi*sqrt(n/3)) * Gamma(1/3) / (4 * 3^(1/3) * Pi^(2/3) * n^(2/3)). - Vaclav Kotesovec, May 21 2018

Maple

seq(coeff(series(mul(1/(1-x^(3*k-1)), k=1..n)*mul(1/(1-x^(6*k-5)), k=1..n), x, 70), x, n), n=0..60); # Muniru A Asiru, May 21 2018

Mathematica

CoefficientList[ Series[ Product[1/(1 - x^(3k -1)), {k, 18}]*Product[1/(1 - x^(6k -5)), {k, 9}], {x, 0, 54}], x] (* Robert G. Wilson v, May 20 2018 *)

Crossrefs

Cf. A035386, A109701, A304885.

Sequence in context: A317177 A326491 A266748 * A280663 A052816 A122130

Adjacent sequences: A304880 A304881 A304882 * A304884 A304885 A304886

Keyword

nonn

Author

Seiichi Manyama, May 20 2018

Status

approved