OFFSET
0,2
COMMENTS
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)
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 528.
FORMULA
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)
MAPLE
seq( 6^n*n!, n=0..20); # G. C. Greubel, Jun 08 2020
MATHEMATICA
Table[6^n n!, {n, 0, 20}] (* Harvey P. Dale, Mar 30 2018 *)
PROG
(Magma) [6^n*Factorial(n): n in [0..20]]; // Vincenzo Librandi, Oct 05 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Joe Keane (jgk(AT)jgk.org)
EXTENSIONS
Name changed by Arkadiusz Wesolowski, Oct 04 2011
STATUS
approved