A051189 Octo-factorial numbers.

1, 8, 128, 3072, 98304, 3932160, 188743680, 10569646080, 676457349120, 48704929136640, 3896394330931200, 342882701121945600, 32916739307706777600, 3423340888001504870400, 383414179456168545484800

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

For n >= 1, a(n) is the order of the wreath product of the symmetric group S_n and the Abelian group (C_8)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001

Number of n X n monomial matrices whose nonzero entries are unit quaternions.

Number of ways of reassembling n slices of toast or of binding n square pages. - Donald S. McDonald, Sep 24 2005

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000165, A034976, A047058, A051188, A053115.

Shifted absolute values are column 1 of A051187.

Programs

Magma

[8^n*Factorial(n): n in [0..20]]; // Vincenzo Librandi, Oct 05 2011

Mathematica

Table[n! 8^n,{n,0,20}] (* Harvey P. Dale, Aug 14 2021 *)

SageMath

[8^n*factorial(n) for n in range(40)] # G. C. Greubel, Oct 21 2022

Formula

a(n) = 8*A034976(n) = Product_{k=1..n} 8*k, n >= 1; a(0) = 1.

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

E.g.f.: 1/(1-8*x).

G.f.: 1/(1 - 8*x/(1 - 8*x/(1 - 16*x/(1 - 16*x/(1 - 24*x/(1 - 24*x/(1 - 32*x/(1 - 32*x/(1 - ... (continued fraction). - Philippe Deléham, Jan 07 2012

From Amiram Eldar, Jun 25 2020: (Start)

Sum_{n>=0} 1/a(n) = e^(1/8).

Sum_{n>=0} (-1)^n/a(n) = e^(-1/8). (End)