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.

A294319 a(n) = Product_{k=0..n} (3*k + 2)!.

Original entry on oeis.org

2, 240, 9676800, 386266890240000, 33674087438261157888000000, 11977449554394932435557703221248000000000, 29139961073721833036780987632259240162985246720000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

Crossrefs

Cf. A268504, A294318.

Programs

  • Mathematica
    Table[Product[(3*k + 2)!, {k, 0, n}] , {n, 0, 10}]
FoldList[Times,(3 Range[0,10]+2)!] (* Harvey P. Dale, Sep 26 2023 *)

Formula

a(n) ~ 3^(3*n^2/2 + 4*n + 101/36) * (2*Pi)^(n/2 + 1/3) * n^(3*n^2/2 + 4*n + 91/36) * Gamma(1/3)^(1/3) / (A^(1/3) * exp(9*n^2/4 + 4*n - 1/36)), where A is the Glaisher-Kinkelin constant A074962.
A268504(n) * A294318(n) * A294319(n) = A000178(3*n + 2).

A294320 a(n) = Product_{k=0..n} (4*k + 1)!.

Original entry on oeis.org

1, 120, 43545600, 271159356948480000, 96447974277170077976494080000000, 4927617876373416030299815278723491640115200000000000, 76433315893700635598991132508610825923227961061372903345356800000000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

Crossrefs

Cf. A168467, A268505, A294318, A294321, A294322.

Programs

  • Mathematica
    Table[Product[(4*k + 1)!, {k, 0, n}] , {n, 0, 10}]

Formula

a(n) ~ 2^(4*n^2 + 15*n/2 + 10/3) * n^(2*n^2 + 7*n/2 + 65/48) * Pi^(n/2 + 3/4) / (A^(1/4) * Gamma(1/4)^(1/2) * exp(3*n^2 + 7*n/2 - 1/48)), where A is the Glaisher-Kinkelin constant A074962.
A268505(n) * A294320(n) * A294321(n) * A294322(n) = A000178(4*n + 3).

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 1-3 of 3 results.

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