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 1-5 of 5 results.

A271946 a(n) = Product_{k=0..n} (6*k)!.

Original entry on oeis.org

1, 720, 344881152000, 2208058019165981638656000000, 1369986068925795885347091500568179543900160000000000, 363392722685428853076589064611759104109572860599125858715484081356800000000000000000
Offset: 0

Views

Author

Vaclav Kotesovec, Apr 17 2016

Keywords

Comments

The next term has 126 digits.
Partial products of A195390. - Michel Marcus, Jul 06 2019

Links

Crossrefs

Cf. A000178, A098694, A195390, A268504, A268505, A268506, A271947.

Programs

  • Mathematica
    Table[Product[(6*k)!,{k,0,n}],{n,0,8}]
  • PARI
    {a(n) = prod(k=1, n, (6*k)!)} \\ Seiichi Manyama, Jul 06 2019

Formula

a(n) ~ A^(-1/6) * exp(1/72 - 7*n/2 - 9*n^2/2) * n^(55/72 + 7*n/2 + 3*n^2) * 2^(1/72 + 4*n + 3*n^2) * 3^(47/72 + 7*n/2 + 3*n^2) * Pi^(n/2 - 1/3) * Gamma(1/3)^(5/3), where A = A074962 is the Glaisher-Kinkelin constant.

A195391 a(n) = (7*n)!.

Original entry on oeis.org

1, 5040, 87178291200, 51090942171709440000, 304888344611713860501504000000, 10333147966386144929666651337523200000000, 1405006117752879898543142606244511569936384000000000, 608281864034267560872252163321295376887552831379210240000000000, 710998587804863451854045647463724949736497978881168458687447040000000000000
Offset: 0

Views

Author

Vincenzo Librandi, Sep 24 2011

Keywords

Links

Crossrefs

Cf. A000152, A010050, A100732, A100733, A100734, A195390, A271947.

Programs

A195392 a(n) = (8*n)!.

Original entry on oeis.org

1, 40320, 20922789888000, 620448401733239439360000, 263130836933693530167218012160000000, 815915283247897734345611269596115894272000000000, 12413915592536072670862289047373375038521486354677760000000000, 710998587804863451854045647463724949736497978881168458687447040000000000000
Offset: 0

Views

Author

Vincenzo Librandi, Sep 24 2011

Keywords

Links

Crossrefs

Cf. A000152, A010050, A100732, A100733, A100734, A195390, A195391

Programs

  • Magma
    [Factorial(8*n): n in [0..10]];
  • Mathematica
    (8*Range[0, 8])! (* Paolo Xausa, Aug 12 2025 *)

A195393 a(n) = (9*n)!.

Original entry on oeis.org

1, 362880, 6402373705728000, 10888869450418352160768000000, 371993326789901217467999448150835200000000, 119622220865480194561963161495657715064383733760000000000
Offset: 0

Views

Author

Vincenzo Librandi, Sep 24 2011

Keywords

Links

Crossrefs

Cf. A000152, A010050, A100732, A100733, A100734, A195390, A195391, A195392.

Programs

  • Magma
    [Factorial(9*n): n in [0..10]];
  • Mathematica
    (9Range[0,10])! (* Harvey P. Dale, Jan 25 2023 *)

A195394 a(n) = (10*n)!

Original entry on oeis.org

1, 3628800, 2432902008176640000, 265252859812191058636308480000000, 815915283247897734345611269596115894272000000000, 30414093201713378043612608166064768844377641568960512000000000000
Offset: 0

Views

Author

Vincenzo Librandi, Sep 24 2011

Keywords

Crossrefs

Cf. A000142, A008592, A010050, A100732, A100733, A100734, A195390, A195391, A195392, A195393.
Cf. A195070, A196498.

Programs

  • Magma
    [Factorial(10*n): n in [0..10]];
  • Mathematica
    a[n_] := (10*n)!; Array[a, 6, 0] (* Amiram Eldar, Apr 03 2021 *)
(10*Range[0,10])! (* Harvey P. Dale, Aug 04 2025 *)

Formula

From Amiram Eldar, Apr 03 2021: (Start)
a(n) = A000142(A008592(n)).
Sum_{n>=0} 1/a(n) = A195070.
Sum_{n>=0} (-1)^n/a(n) = A196498. (End)
Showing 1-5 of 5 results.

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

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