A092515 -id:A092515 - 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

A092727 Decimal expansion of e^(-1/6).

Original entry on oeis.org

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

Offset: 0

Mohammad K. Azarian, Apr 22 2004

			0.84648172489061407404491739979875457688829162442705...

Cf. A001113, A019774, A068985, A092515 (reciprocal).

RealDigits[E^-(1/6),10,120][[1]] (* Harvey P. Dale, Jun 18 2012 *)

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

cp's OEIS Frontend

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

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