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.

A272164 a(n) = Product_{k=0..n} (n^2-k)!.

Original entry on oeis.org

1, 1, 288, 53094139822080000, 7114507432973653690572666462301501337370624000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 21 2016

Keywords

Comments

The next term has 392 digits.

Crossrefs

Programs

  • Mathematica
    Table[Product[(n^2-k)!, {k, 0, n}], {n, 0, 6}]
    Table[BarnesG[n^2 + 2]/BarnesG[n^2 - n + 1], {n, 0, 6}]

Formula

a(n) = A272163(n) * ((n^2)!)^(n+1) / A272179(n)^n.
a(n) ~ exp(1/24 + n/6 - n^2 - n^3) * n^(1 + n^2 + 2*n^3) * (2*Pi)^((n+1)/2).

A272163 a(n) = Product_{k=0..n} (n^2-k)^k.

Original entry on oeis.org

0, 12, 84672, 133937556480, 84132174409113600000, 31820251569524195280814080000000, 10171374668270380199596141241071328726876160000, 3665849746122305381874580384965936229566478146157181833052160000
Offset: 1

Views

Author

Vaclav Kotesovec, Apr 21 2016

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Product[(n^2-k)^k, {k, 0, n}], {n, 1, 10}]
    Table[BarnesG[n^2 + 2] * (n-1)^n * n^n * Pochhammer[1 - n + n^2, n]^n / (((n^2)!)^(n+1) * BarnesG[n^2 - n + 1]), {n, 1, 10}]

Formula

a(n) = A272164(n) * A272179(n)^n / ((n^2)!)^(n+1).
a(n) ~ n^(n*(n+1)) / exp(n/3 + 5/8).

A272180 a(n) = Product_{k=0..n} (n^2 + k).

Original entry on oeis.org

0, 2, 120, 11880, 1860480, 427518000, 135970773120, 57274321104000, 30885807297945600, 20759078324729606400, 17018214378110225280000, 16716468557742686853120000, 19383353274717848149493760000, 26198415087179810897268887040000, 40828604361516687201839617904640000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 21 2016

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Product[n^2 + k, {k, 0, n}], {n, 0, 15}]
    Table[n^2*Pochhammer[1 + n^2, n], {n, 0, 15}]

Formula

a(n) ~ exp(1/2) * n^(2*n + 2).
Showing 1-3 of 3 results.