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 1-4 of 4 results.

A294322 a(n) = Product_{k=0..n} (4*k + 3)!.

Original entry on oeis.org

6, 30240, 1207084032000, 1578472848668491776000000, 192013488168893760607534429765632000000000, 4963935910233933921764132479991824059486720994836480000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

Crossrefs

Cf. A268505, A294320, A294321, A294325.

Programs

  • Mathematica
    Table[Product[(4*k + 3)!, {k, 0, n}] , {n, 0, 10}]

Formula

a(n) ~ 2^(4*n^2 + 23*n/2 + 47/6) * n^(2*n^2 + 11*n/2 + 173/48) * Pi^(n/2 + 1/4) * Gamma(1/4)^(1/2) / (A^(1/4) * exp(3*n^2 + 11*n/2 - 1/48)), where A is the Glaisher-Kinkelin constant A074962.
A268505(n) * A294320(n) * A294321(n) * A294322(n) = A000178(4*n + 3).

A294324 a(n) = Product_{k=0..n} (5*k + 2)!.

Original entry on oeis.org

2, 10080, 4828336128000, 1717378459351319052288000000, 1930334638180469242638816526565470371840000000000, 21019161870767674789722561439867977128887689291877548419973120000000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

Crossrefs

Cf. A268506, A294319, A294321, A294323, A294325, A294326.

Programs

  • Mathematica
    Table[Product[(5*k + 2)!, {k, 0, n}] , {n, 0, 10}]
FoldList[Times,(5Range[0,10]+2)!] (* Harvey P. Dale, Aug 11 2024 *)

Formula

a(n) ~ 2^(n/2 + 6/5) * 5^(5*n^2/2 + 5*n + 7/3) * n^(5*n^2/2 + 5*n + 137/60) * Pi^(n/2 + 11/10) / (A^(1/5) * (1 + sqrt(5))^(1/10) * Gamma(1/5)^(2/5) * Gamma(2/5)^(4/5) * exp(15*n^2/4 + 5*n - 1/60)), where A is the Glaisher-Kinkelin constant A074962.
A268506(n) * A294323(n) * A294324(n) * A294325(n) * A294326(n) = A000178(5*n+4).

A294326 a(n) = Product_{k=0..n} (5*k + 4)!.

Original entry on oeis.org

24, 8709120, 759246199455744000, 92358580167818066670290731008000000, 57303733451473984666829812178837795780510487674880000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

Crossrefs

Cf. A268506, A294323, A294324, A294325.

Programs

  • Mathematica
    Table[Product[(5*k + 4)!, {k, 0, n}] , {n, 0, 10}]
FoldList[Times,(5*Range[0,5]+4)!] (* Harvey P. Dale, Sep 27 2018 *)

Formula

a(n) ~ 2^(n/2 + 1/5) * 5^(5*n^2/2 + 7*n + 29/6) * n^(5*n^2/2 + 7*n + 281/60) * Pi^(n/2 + 1/10) * Gamma(1/5)^(3/5) * Gamma(2/5)^(1/5) / (A^(1/5) * (1 + sqrt(5))^(1/10) * exp(15*n^2/4 + 7*n-1/60)), where A is the Glaisher-Kinkelin constant A074962.
A268506(n) * A294323(n) * A294324(n) * A294325(n) * A294326(n) = A000178(5*n+4).

A294323 a(n) = Product_{k=0..n} (5*k + 1)!.

Original entry on oeis.org

1, 720, 28740096000, 601322989968949248000000, 30722158107023001697205508762501120000000000, 12389984031943899068723274670059592852478855603111854080000000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

Crossrefs

Cf. A168467, A268506, A294318, A294320, A294324, A294325, A294326.

Programs

  • Mathematica
    Table[Product[(5*k + 1)!, {k, 0, n}] , {n, 0, 10}]

Formula

a(n) ~ 2^(n/2 + 7/10) * 5^(5*n^2/2 + 4*n + 4/3) * n^(5*n^2/2 + 4*n + 83/60) * Pi^(n/2 + 3/5) * Gamma(2/5)^(1/5) / (A^(1/5) * (1 + sqrt(5))^(1/10) * Gamma(1/5)^(2/5) * exp(15*n^2/4 + 4*n - 1/60)), where A is the Glaisher-Kinkelin constant A074962.
A268506(n) * A294323(n) * A294324(n) * A294325(n) * A294326(n) = A000178(5*n+4).
Showing 1-4 of 4 results.

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