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.

A347898 E.g.f.: Product_{k>=1} (1 + x^k)^(sin(x)/k).

Original entry on oeis.org

1, 0, 2, 0, 24, -30, 694, -1050, 37832, -167076, 3840946, -16352820, 484077316, -3571377810, 92305923462, -735565382370, 24089429290352, -260389373957160, 7612771211634930, -88060997260644552, 2819270530524656316, -42624237378570669990, 1487399781900667121150
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)^(sin(x)/k))))

A347900 E.g.f.: Product_{k>=1} (1 + x^k)^(tan(x)/k).

Original entry on oeis.org

1, 0, 2, 0, 36, -30, 1384, -1680, 95120, -269136, 10673176, -39346560, 1646512480, -9198926880, 351447935136, -2475812561040, 99060435898112, -904912972938240, 34772619691749120, -378998950170136320, 14965802767502028672, -197854178189523770880, 7940955462403332290816
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)/k))))

A347893 E.g.f.: Product_{k>=1} (1 + x^k)^cos(x).

Original entry on oeis.org

1, 1, 2, 9, 30, 195, 1545, 12474, 95564, 1199397, 14287845, 167518846, 2341450386, 34489552331, 540927170147, 10114629115798, 175935142966408, 3184271322683385, 68623817313870153, 1442553498798565142, 31856896467060026670, 787164874800260366287, 19097783293834170329239
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)^cos(x))))
    
  • PARI
    N=40; x='x+O('x^N); Vec(serlaplace(exp(cos(x)*sum(k=1, N, sigma(k>>valuation(k, 2))*x^k/k))))

Formula

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