A304883 - OEIS

%I #27 May 21 2018 06:43:41

%S 1,1,2,2,3,4,5,7,9,11,14,17,21,26,32,39,47,56,67,80,95,113,133,156,

%T 183,214,250,291,338,391,452,521,600,690,791,906,1035,1181,1346,1532,

%U 1741,1975,2238,2532,2862,3231,3643,4103,4615,5186,5822,6529,7315,8187,9154

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

%H Sylvie Corteel, Carla D. Savage, and Andrew V. Sills. F. Beukers, <a href="https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/175/">Lecture hall sequences, q-series, and asymmetric partition identities</a>, In Alladi K., Garvan F. (eds) Partitions, q-Series, and Modular Forms pp 53-68. Developments in Mathematics, vol 23. Springer, New York, NY.

%F 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)).

%F 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

%p 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

%t 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 *)

%Y Cf. A035386, A109701, A304885.

%K nonn

%O 0,3

%A _Seiichi Manyama_, May 20 2018