A051188 Sept-factorial numbers.

1, 7, 98, 2058, 57624, 2016840, 84707280, 4150656720, 232436776320, 14643516908160, 1025046183571200, 78928556134982400, 6629998715338521600, 603329883095805465600, 59126328543388935628800

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_7)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 614.
• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000142, A000165, A032031, A045754, A047053, A047058, A049209, A051186, A052562, A053106, A084947, A092516, A092750, A144827, A144739, A147585.

Programs

Magma

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

PARI

a(n) = n!*7^n; \\ Michel Marcus, Jun 08 2020

Formula

a(n) = n!*7^n =: (7*n)(!^7).

a(n) = 7*A034834(n) = Product_{k=1..n} 7*k, n >= 1.

E.g.f.: 1/(1 - 7*x).

G.f.: 1/(1 - 7*x/(1 - 7*x/(1 - 14*x/(1 - 14*x/(1 - 21*x/(1 - 21*x/(1 - 28*x/(1 - 28*x/(1 - ... (continued fraction). - Philippe Deléham, Jan 08 2012

From Amiram Eldar, Jun 25 2020: (Start)

Sum_{n>=0} 1/a(n) = e^(1/7) (A092516).

Sum_{n>=0} (-1)^n/a(n) = e^(-1/7) (A092750). (End)