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.

Showing 1-2 of 2 results.

A285214 Expansion of Product_{k>=0} (1-x^(5*k+4))^(5*k+4).

Original entry on oeis.org

1, 0, 0, 0, -4, 0, 0, 0, 6, -9, 0, 0, -4, 36, -14, 0, 1, -54, 92, -19, 0, 36, -228, 202, -24, -9, 272, -702, 358, -29, -158, 1168, -1696, 598, 2, -1027, 3810, -3605, 904, 423, -4600, 10196, -6898, 1240, 2990, -15805, 24104, -12242, 822, 14005, -46090, 51376
Offset: 0

Views

Author

Seiichi Manyama, Apr 15 2017

Keywords

Links

Crossrefs

Product_{k>=0} (1-x^(m*k+m-1))^(m*k+m-1): A285069 (m=2), A285212 (m=3), A285213 (m=4), this sequence (m=5).
Cf. A285132.

Programs

  • Mathematica
    nmax = 100; CoefficientList[Series[Product[(1-x^(5*k+4))^(5*k+4), {k,0,nmax}], {x,0,nmax}], x] (* Vaclav Kotesovec, Apr 15 2017 *)
  • PARI
    x='x+O('x^100); Vec(prod(k=0, 100, (1 - x^(5*k + 4))^(5*k + 4))) \\ Indranil Ghosh, Apr 15 2017

A285131 Expansion of Product_{k>=0} 1/(1-x^(4*k+3))^(4*k+3).

Original entry on oeis.org

1, 0, 0, 3, 0, 0, 6, 7, 0, 10, 21, 11, 15, 42, 61, 36, 70, 150, 150, 124, 278, 441, 375, 468, 909, 1131, 1018, 1581, 2602, 2810, 2947, 4819, 6768, 6980, 8509, 13389, 16788, 17609, 23722, 34720, 40337, 44863, 63128, 85430, 95887, 114037, 159882, 202699, 227087
Offset: 0

Views

Author

Seiichi Manyama, Apr 15 2017

Keywords

Links

Crossrefs

Product_{k>=0} 1/(1-x^(m*k+m-1))^(m*k+m-1): A262811 (m=2), A262946 (m=3), this sequence (m=4), A285132 (m=5).
Cf. A285213.

Programs

  • Mathematica
    nmax = 100; CoefficientList[Series[Product[1/(1-x^(4*k+3))^(4*k+3), {k,0,nmax}], {x,0,nmax}], x] (* Vaclav Kotesovec, Apr 15 2017 *)
  • PARI
    x='x+O('x^100); Vec(prod(k=0, 100, 1/(1 - x^(4*k + 3))^(4*k + 3))) \\ Indranil Ghosh, Apr 15 2017

Formula

a(n) ~ exp(4*c + 3 * 2^(-4/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(11/72) / (2^(47/72) * sqrt(3) * Gamma(3/4) * n^(47/72)), where c = Integral_{x=0..inf} ((5/(exp(x)*96) + 1/(exp(3*x)*(1 - exp(-4*x))^2) - 1/(16*x^2) - 1/(16*x))/x) dx = -0.158924147180165035059952001737321408554746599955833696821824808... - Vaclav Kotesovec, Apr 15 2017
Showing 1-2 of 2 results.

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