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.

A294325 a(n) = Product_{k=0..n} (5*k + 3)!.

Original entry on oeis.org

6, 241920, 1506440871936000, 9644797427717007797649408000000, 249337464544494851133170653103408676989829120000000000, 76020086814652932482688746849816272353956621412690696880710462996480000000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

Crossrefs

Cf. A268506, A294322, A294323, A294324, A294326.

Programs

  • Mathematica
    Table[Product[(5*k + 3)!, {k, 0, n}] , {n, 0, 10}]

Formula

a(n) ~ (1 + sqrt(5))^(2/5) * Gamma(2/5)^(1/5) * 2^(n/2 + 1/5) * 5^(5*n^2/2 + 6*n + 43/12) * n^(5*n^2/2 + 6*n + 203/60) * Pi^(n/2 + 3/5) / (A^(1/5) * Gamma(1/5)^(2/5) * exp(15*n^2/4 + 6*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).

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).

A294321 a(n) = Product_{k=0..n} (4*k + 2)!.

Original entry on oeis.org

2, 1440, 5225472000, 455547719673446400000, 2916586742141623158009180979200000000, 3278245620793706216637861108629164518335840256000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

Crossrefs

Cf. A268505, A294319, A294320, A294322, A294324.

Programs

  • Mathematica
    Table[Product[(4*k + 2)!, {k, 0, n}] , {n, 0, 10}]

Formula

a(n) ~ 2^(4*n^2 + 19*n/2 + 35/6) * n^(2*n^2 + 9*n/2 + 113/48) * Pi^(n/2 + 3/4) / (A^(1/4) * Gamma(1/4)^(1/2) * exp(3*n^2 + 9*n/2 - 1/48)), where A is the Glaisher-Kinkelin constant A074962.
A268505(n) * A294320(n) * A294321(n) * A294322(n) = A000178(4*n + 3).

A365266 a(n) = Product_{k=1..n} Gamma(6*k).

Original entry on oeis.org

1, 120, 4790016000, 1703748471578689536000000, 44045334006101976766560297729172439040000000000, 389438360216723307909581902233109465138002465491175688781168640000000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Sep 01 2023

Keywords

Crossrefs

Cf. A000178, A168467, A294319, A294322, A294326.
Cf. A055462, A306635, A306651.

Programs

  • Mathematica
    Table[Product[Gamma[6*k], {k, 1, n}], {n, 0, 10}]
Table[Product[(6*k-1)!, {k, 1, n}], {n, 0, 10}]

Formula

a(n) = A^(35/6) * exp(-35/72) * Gamma(1/3)^(5/3) * 2^(-125/72 + 3*n^2) * 3^(47/72 + 5*n/2 + 3*n^2) * Pi^(-25/12 - 5*n/2) * BarnesG(1 + n) * BarnesG(7/6 + n) * BarnesG(4/3 + n) * BarnesG(3/2 + n) * BarnesG(5/3 + n) * BarnesG(11/6 + n), where A = A074962 is the Glaisher-Kinkelin constant.
a(n) ~ A^(-1/6) * Gamma(1/3)^(5/3) * 2^(-35/72 + 3*n + 3*n^2) * 3^(47/72 + 5*n/2 + 3*n^2) * exp(1/72 - 5*n/2 - 9*n^2/2) * n^(19/72 + 5*n/2 + 3*n^2) * Pi^(-5/6 + n/2), where A = A074962 is the Glaisher-Kinkelin constant.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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