cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A304885 #29 May 29 2024 13:46:54
%S A304885 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,
%T A304885 124,144,166,191,220,252,289,331,378,431,490,557,632,717,812,917,1035,
%U A304885 1167,1315,1480,1663,1866,2092,2344,2624,2934,3277,3656,4076,4542,5056
%N A304885 Expansion of Product_{k>=1} 1/(1-x^(3*k-2)) * Product_{k>=1} 1/(1-x^(6*k-1)).
%H A304885 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 A304885 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)).
%F A304885 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
%p A304885 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
%t A304885 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 *)
%Y A304885 Cf. A035382, A109702, A304883.
%K A304885 nonn
%O A304885 0,5
%A A304885 _Seiichi Manyama_, May 20 2018