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 1-7 of 7 results.

A088020 a(n) = (n^2)!.

Original entry on oeis.org

1, 1, 24, 362880, 20922789888000, 15511210043330985984000000, 371993326789901217467999448150835200000000, 608281864034267560872252163321295376887552831379210240000000000
Offset: 0

Views

Author

Hugo Pfoertner, Sep 18 2003

Keywords

Comments

a(n) is the number of ways in which is possible to fill an n X n square matrix with n^2 distinct elements. - Stefano Spezia, Sep 16 2018

Links

Crossrefs

Cf. A000142 (n!), A000290 (n^2).
Cf. A039622, A179268. - Reinhard Zumkeller, Jul 06 2010
Cf. A272094, A272095, A272164.

Programs

  • GAP
    List([0..10],n->Factorial(n^2)); # Muniru A Asiru, Sep 17 2018
  • Magma
    [Factorial(n^2): n in [0..10]]; // Vincenzo Librandi, May 31 2011
  • Maple
    seq(factorial(n^2),n=0..10); # Muniru A Asiru, Sep 17 2018
  • Mathematica
    Table[(n^2)!,{n,0,9}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
  • PARI
    for(n=0,10,print1((n^2)!,",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Oct 22 2006

A272095 a(n) = Product_{k=0..n} binomial(n^2,k).

Original entry on oeis.org

1, 1, 24, 27216, 1956864000, 11593630125000000, 7004354761049263478784000, 515246658615545697034849051407876096, 5368556637668593177532650186945239827409750982656, 9038577429104951379916309583338181472480254559457860096000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 20 2016

Keywords

Crossrefs

Cf. A272093, A272094, A272241.
Cf. A000178, A098694, A268196, A262261.

Programs

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

Formula

a(n) = ((n^2)!)^(n+1) / (A272164(n) * A000178(n)).
a(n) ~ A * exp(3*n^2/4 + 5*n/6 - 1/8) * n^(n^2/2 - 5/12) / (2*Pi)^((n+1)/2), where A = A074962 is the Glaisher-Kinkelin constant.

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

Cf. A272164, A272237.

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).

A272238 a(n) = Product_{k=0..n} (n^2+k)!.

Original entry on oeis.org

1, 2, 2073600, 25177856146146034974720000000, 14100949826093501607549529280892932893801777581548587107609477120000000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2016

Keywords

Comments

The next term has 173 digits.

Crossrefs

Cf. A135860, A272164, A272180, A272237, A272241.

Programs

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

Formula

a(n) = ((n^2+n)!)^(n+1) / A272237(n).
a(n) ~ exp(11/24 + n/6 - n^2 - n^3) * n^((1+n)*(1 + n + 2*n^2)) * (2*Pi)^((n+1)/2).

A272241 a(n) = Product_{k=0..n} ((n^2 + k)! / (n^2 - k)!).

Original entry on oeis.org

1, 2, 7200, 474211584000, 1981999450972492922880000, 1401219961854040654113268364083200000000000, 370389015130516478011776928922387124162707119541939129548800000000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 23 2016

Keywords

Comments

The next term has 95 digits.

Crossrefs

Cf. A103207, A272164, A272238, A371642.

Programs

  • Mathematica
    Table[Product[(n^2+k)!/(n^2-k)!,{k,0,n}],{n,0,7}]
Table[BarnesG[n^2 - n + 1]*BarnesG[n^2 + n + 2]/(BarnesG[n^2 + 2]*BarnesG[n^2 + 1]), {n, 0, 6}]

Formula

a(n) = A272238(n) / A272164(n).
a(n) ~ exp(5/12) * n^(2*n*(n+1)).

A272179 a(n) = Product_{k=0..n} (n^2 - k).

Original entry on oeis.org

0, 0, 24, 3024, 524160, 127512000, 42072307200, 18183435621120, 9993927307714560, 6816310367682816000, 5653408585997652480000, 5606015030436835542528000, 6551662594343454506664345600, 8914054345090074511550572953600, 13970892529731225585461744812032000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 21 2016

Keywords

Crossrefs

Cf. A272163, A272164, A272180.

Programs

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

Formula

a(n) ~ exp(-1/2) * n^(2*n + 2).

A362187 a(n) = (n^2 - n)!.

Original entry on oeis.org

1, 1, 2, 720, 479001600, 2432902008176640000, 265252859812191058636308480000000, 1405006117752879898543142606244511569936384000000000, 710998587804863451854045647463724949736497978881168458687447040000000000000
Offset: 0

Views

Author

Stefano Spezia, Apr 10 2023

Keywords

Comments

The next term has 104 digits.
For n > 0, a(n) is the number of n X n matrices using all the integers from 1 to n^2 and having the main diagonal given.

Links

Crossrefs

Cf. A000142, A000290, A002378, A088020.
Cf. A039622, A179268, A272094, A272095, A272164.
Cf. A362209.

Programs

  • Mathematica
    a[n_]:=(n^2-n)!; Array[a,9,0]

Formula

a(n) = (n^2 - n)*a(n-1) for n > 1.
a(n) = A000142(A002378(n-1)) for n > 0.
Showing 1-7 of 7 results.

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

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