A092750 -id:A092750 - cp's OEIS frontend

A051188 Sept-factorial numbers.

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

Offset: 0

Wolfdieter Lang

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

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

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

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

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

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)

A029574 Number of permutations of an n-set containing a 7-cycle.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 720, 5760, 51840, 518400, 5702400, 68428800, 889574400, 11564467200, 173467008000, 2775472128000, 47183026176000, 849294471168000, 16136594952192000, 322731899043840000, 6802195410616320000, 149648299033559040000, 3441910877771857920000

Offset: 0

Rob Pratt

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..450

Column k=7 of A293211.

a(n) = n! * (1 - sum(k=0, floor(n/7), (-1)^k/(k!*7^k) ) ); \\ Michel Marcus, Aug 08 2013

a(n) = n! * (1 - sum_{k=0..floor(n/7)} (-1)^k/(k!*7^k)).
a(n)/n! is asymptotic to 1-e^(-1/7) =  1 - A092750.
E.g.f.: (1-exp(-x^7/7))/(1-x). - Alois P. Heinz, Oct 11 2017

cp's OEIS Frontend

A051188 Sept-factorial numbers.

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