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A304883
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Expansion of Product_{k>=1} 1/(1-x^(3*k-1)) * Product_{k>=1} 1/(1-x^(6*k-5)).
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1
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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
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OFFSET
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0,3
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LINKS
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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.
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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