A092727 -id:A092727 - cp's OEIS frontend

A047058 a(n) = 6^n * n!.

1, 6, 72, 1296, 31104, 933120, 33592320, 1410877440, 67722117120, 3656994324480, 219419659468800, 14481697524940800, 1042682221795737600, 81329213300067532800, 6831653917205672755200, 614848852548510547968000

Offset: 0

Joe Keane (jgk(AT)jgk.org)

For n >= 1, a(n) is the order of the wreath product of the symmetric group S_n and the Abelian group (C_6)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001
a(n) is the number of ways 3 members of each of n different teams can be arranged in a row so that members of the same team are together. - Geoffrey Critzer, Mar 30 2009
From Jianing Song, Mar 29 2021: (Start)
Number of n X n monomial matrices with entries 0, +/-1, +/-w, +/-w^2, where w = (-1 + sqrt(3)*i)/2 is a primitive 3rd root of unity.
a(n) is the order of the group U_n(Z[w]) = {A in M_n(Z[w]): A*A^H = I_n}, the group of n X n unitary matrices over the Eisenstein integers. Here A^H is the conjugate transpose of A. (End)

Vincenzo Librandi, Table of n, a(n) for n = 0..300
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 528.

Cf. A000142, A000165, A008542, A008543, A047053, A051151, A053103, A092515, A092727.

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

seq( 6^n*n!, n=0..20); # G. C. Greubel, Jun 08 2020

Table[6^n n!,{n,0,20}] (* Harvey P. Dale, Mar 30 2018 *)

a(n) = A051151(n+1, 0).
E.g.f.: 1/(1 - 6*x).
G.f.: 1/(1 -6*x/(1 - 6*x/(1 - 12*x/(1 - 12*x/(1 - 18*x/(1 - 18*x/(1 - 24*x/(1 - 24*x/(1 - 30*x/(1 - 30*x/(1 -... (continued fraction). - Philippe Deléham, Jan 08 2012
From Amiram Eldar, Jun 25 2020: (Start)
Sum_{n>=0} 1/a(n) = e^(1/6) (A092515).
Sum_{n>=0} (-1)^n/a(n) = e^(-1/6) (A092727). (End)

Name changed by Arkadiusz Wesolowski, Oct 04 2011

A092515 Decimal expansion of e^(1/6).

Original entry on oeis.org

1, 1, 8, 1, 3, 6, 0, 4, 1, 2, 8, 6, 5, 6, 4, 5, 9, 8, 0, 3, 0, 5, 1, 1, 2, 1, 5, 2, 5, 0, 7, 1, 8, 4, 3, 2, 7, 8, 3, 0, 1, 8, 9, 3, 1, 0, 8, 3, 8, 9, 6, 3, 7, 9, 7, 8, 5, 6, 1, 9, 4, 2, 8, 0, 2, 2, 6, 4, 5, 5, 2, 8, 5, 5, 9, 2, 2, 9, 7, 4, 5, 6, 6, 2, 3, 6, 6, 9, 7, 3, 8, 5, 0, 4, 4, 2, 7, 6, 3, 1, 9, 1, 7, 7, 2

Offset: 1

Mohammad K. Azarian, Apr 05 2004

e^(1/6) maximizes the value of x^(c/(x^6)) for any real positive constant c, and minimizes for it for a negative constant, on the range x > 0. - A.H.M. Smeets, Aug 16 2018

			1.18136041286564598030511215250718432783018931083896...

Muniru A Asiru, Table of n, a(n) for n = 1..2000

Cf. A001113, A019774, A092727 (reciprocal).

evalf(exp(1/6)); # Muniru A Asiru, Aug 16 2018

RealDigits[E^(1/6),10,120][[1]] (* Harvey P. Dale, Sep 13 2011 *)

PARI
```
exp(1/6) \\ Michel Marcus, Aug 16 2018
```

Equals lim_{x->0} (sinh(x)/x)^(1/x^2). - Amiram Eldar, Jul 04 2022

A029573 Number of permutations of an n-set containing a 6-cycle.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 120, 840, 6720, 60480, 604800, 6652800, 73180800, 951350400, 13318905600, 199783584000, 3196537344000, 54341134848000, 983080530432000, 18678530078208000, 373570601564160000, 7844982632847360000, 172589617922641920000, 3969561212220764160000

Offset: 0

Rob Pratt

nonn

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

Column k=6 of A293211.

a(n) = n! * (1 - sum(k=0, floor(n/6), (-1)^k/(k!*6^k) ) ); \\ Michel Marcus, Aug 08 2013

a(n) = n! * (1 - sum_{k=0..floor(n/6)} (-1)^k/(k!*6^k)).
a(n)/n! is asymptotic to 1-e^(-1/6) = 1 - A092727.
E.g.f.: (1-exp(-x^6/6))/(1-x). - Alois P. Heinz, Oct 11 2017

cp's OEIS Frontend

A047058 a(n) = 6^n * n!.

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A092515 Decimal expansion of e^(1/6).

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Links

Crossrefs

Programs

Maple

Mathematica

PARI

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A029573 Number of permutations of an n-set containing a 6-cycle.

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Author

Keywords

Links

Crossrefs

Programs

PARI

Formula