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.

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

Original entry on oeis.org

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

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Author

Seiichi Manyama, May 20 2018

Keywords

Crossrefs

Programs

  • 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 *)

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
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