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.

A301942 Expansion of e.g.f. arcsin(x)/cos(x) (odd powers only).

Original entry on oeis.org

1, 4, 44, 1016, 42384, 2908544, 306305856, 46659144832, 9760451385600, 2683733034474496, 936308392553036800, 403127865773461755904, 209562975305232836300800, 129255511221696545852424192, 93252273300325219683758915584, 77766048645578119241905858314240
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 09 2018

Keywords

Examples

			arcsin(x)/cos(x) = x/1! + 4*x^3/3! + 44*x^5/5! + 1016*x^7/7! + 42384*x^9/9! + ...
		

Crossrefs

Programs

  • Mathematica
    nmax = 16; Table[(CoefficientList[Series[ArcSin[x]/Cos[x], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

Formula

a(n) = (2*n+1)! * [x^(2*n+1)] arcsin(x)/cos(x).

A302444 Expansion of e.g.f. arcsinh(x)/cos(x) (odd powers only).

Original entry on oeis.org

1, 2, 24, 216, 15936, -77056, 90991744, -8523712768, 2731708067840, -684815907467264, 268028469798256640, -114888252320482000896, 62022733722259702579200, -38635369828053720937463808, 28349537098304682205749968896, -23874826868622028919177351004160
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 09 2018

Keywords

Examples

			arcsinh(x)/cos(x) = x/1! + 2*x^3/3! + 24*x^5/5! + 216*x^7/7! + 15936*x^9/9! - 77056*x^11/11! + ...
		

Crossrefs

Programs

  • Mathematica
    nmax = 16; Table[(CoefficientList[Series[ArcSinh[x]/Cos[x], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

Formula

a(n) = (2*n+1)! * [x^(2*n+1)] arcsinh(x)/cos(x).

A302543 Expansion of e.g.f. arctanh(x)/cos(x) (odd powers only).

Original entry on oeis.org

1, 5, 69, 2001, 104073, 8723549, 1088372557, 190057979177, 44285819490065, 13267464006201781, 4964113699657822805, 2266816666007859759489, 1239999748307938170531225, 800189083150907165762837517, 601369618369661775955962338653, 520607107122686183781743903500505
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 09 2018

Keywords

Examples

			arctanh(x)/cos(x) = x/1! + 5*x^3/3! + 69*x^5/5! + 2001*x^7/7! + 104073*x^9/9! + ...
		

Crossrefs

Programs

  • Mathematica
    nmax = 16; Table[(CoefficientList[Series[ArcTanh[x]/Cos[x], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

Formula

a(n) = (2*n+1)! * [x^(2*n+1)] arctanh(x)/cos(x).
Showing 1-3 of 3 results.