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.

A285071 Expansion of Product_{k>=0} (1-x^(5*k+1))^(5*k+1).

Original entry on oeis.org

1, -1, 0, 0, 0, 0, -6, 6, 0, 0, 0, -11, 26, -15, 0, 0, -16, 82, -86, 20, 0, -21, 172, -316, 180, -15, -26, 328, -872, 790, -226, -25, 538, -2043, 2681, -1310, 130, 843, -4184, 7426, -5390, 1365, 1158, -7855, 18067, -17705, 7185, 798, -13701, 39468, -50030
Offset: 0

Views

Author

Seiichi Manyama, Apr 15 2017

Keywords

Links

Crossrefs

Product_{k>=0} (1-x^(m*k+1))^(m*k+1): A285069 (m=2), A285050 (m=3), A285070 (m=4), this sequence (m=5).
Cf. A285049, A285338.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[Product[(1-x^(5*k-4))^(5*k-4), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 17 2017 *)

A285048 Expansion of Product_{k>=0} 1/(1-x^(4*k+1))^(4*k+1).

Original entry on oeis.org

1, 1, 1, 1, 1, 6, 6, 6, 6, 15, 30, 30, 30, 43, 88, 123, 123, 140, 250, 385, 455, 476, 678, 1098, 1413, 1564, 1913, 2918, 4048, 4707, 5452, 7572, 10747, 13265, 15195, 19534, 27349, 35146, 41042, 50011, 67596, 88897, 106519, 126635, 164230, 216862, 266473, 314883
Offset: 0

Views

Author

Seiichi Manyama, Apr 15 2017

Keywords

Links

Crossrefs

Product_{k>=0} 1/(1-x^(m*k+1))^(m*k+1): A262811 (m=2), A262947 (m=3), this sequence (m=4), A285049 (m=5).
Cf. A285070, A285287.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[Product[1/(1-x^(4*k-3))^(4*k-3), {k,1,nmax}], {x,0,nmax}], x] (* Vaclav Kotesovec, Apr 16 2017 *)

Formula

a(n) ~ 4 * Pi * 2^(25/72) * Zeta(3)^(11/72) * exp(4*c + 3 * 2^(-4/3) * Zeta(3)^(1/3) * n^(2/3)) / (sqrt(3) * Gamma(1/4)^3 * n^(47/72)), where c = Integral_{x=0..inf} ((-19/(exp(x)*96) + 1/(exp(x)*(1 - exp(-4*x))^2) - 1/(16*x^2) - 3/(16*x))/x) dx = 0.09601010361866957956805888476415949391295401812706635... - Vaclav Kotesovec, Apr 16 2017
Showing 1-2 of 2 results.

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