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 1-3 of 3 results.

A346841 E.g.f.: Product_{k>=1} 1 / (1 - x^k)^sin(x).

Original entry on oeis.org

1, 0, 2, 9, 40, 360, 2480, 28833, 266936, 3562920, 45634258, 659631225, 10231705196, 176661237948, 3080315922294, 59430009554685, 1217593208993232, 25766943601055184, 583245289316927058, 13861911731632256457, 343615639889119016556, 8925102256331257339140, 242399591002192962709230
Offset: 0

Views

Author

Seiichi Manyama, Sep 18 2021

Keywords

Crossrefs

Programs

  • PARI
    N=40; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^sin(x))))
    
  • PARI
    N=40; x='x+O('x^N); Vec(serlaplace(exp(sin(x)*sum(k=1, N, sigma(k)*x^k/k))))
    
  • PARI
    N=40; x='x+O('x^N); Vec(serlaplace(exp(sin(x)*sum(k=1, N, x^k/(k*(1-x^k))))))

Formula

E.g.f.: exp( sin(x) * Sum_{k>=1} sigma(k)*x^k/k ).
E.g.f.: exp( sin(x) * Sum_{k>=1} x^k/(k*(1 - x^k)) ).

A346941 E.g.f.: Product_{k>=1} 1 / (1 - x^k)^cos(x).

Original entry on oeis.org

1, 1, 4, 15, 90, 555, 4815, 41034, 443268, 4977381, 64274655, 857332366, 13328296014, 207666642131, 3620701556017, 65845797790798, 1294049887432888, 26168756518235801, 576107273399556987, 12940593913711504118, 311924384689270232770, 7752903433736003497447, 203126367130952306670541
Offset: 0

Views

Author

Seiichi Manyama, Sep 18 2021

Keywords

Crossrefs

Programs

  • PARI
    N=40; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^cos(x))))
    
  • PARI
    N=40; x='x+O('x^N); Vec(serlaplace(exp(cos(x)*sum(k=1, N, sigma(k)*x^k/k))))
    
  • PARI
    N=40; x='x+O('x^N); Vec(serlaplace(exp(cos(x)*sum(k=1, N, x^k/(k*(1-x^k))))))

Formula

E.g.f.: exp( cos(x) * Sum_{k>=1} sigma(k)*x^k/k ).
E.g.f.: exp( cos(x) * Sum_{k>=1} x^k/(k*(1 - x^k)) ).

A347894 E.g.f.: Product_{k>=1} (1 + x^k)^tan(x).

Original entry on oeis.org

1, 0, 2, 3, 52, 110, 2690, 11676, 247952, 1434600, 37576168, 296088760, 7698854216, 78083294640, 2187100997328, 27174552638520, 806871808214016, 11698163585372736, 370098862531800000, 6300404006917434624, 208037772410558058624, 4032385785901175122560, 141272996628892396692096
Offset: 0

Views

Author

Seiichi Manyama, Sep 18 2021

Keywords

Crossrefs

Programs

  • PARI
    N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, (1+x^k)^tan(x))))
    
  • PARI
    N=40; x='x+O('x^N); Vec(serlaplace(exp(tan(x)*sum(k=1, N, sigma(k>>valuation(k, 2))*x^k/k))))

Formula

E.g.f.: exp( tan(x) * Sum_{k>=1} x^k / (k*(1 - x^(2*k))) ). - Ilya Gutkovskiy, Sep 18 2021
E.g.f.: exp( tan(x) * Sum_{k>=1} A000593(k)*x^k/k ). - Seiichi Manyama, Sep 18 2021
Showing 1-3 of 3 results.