This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047058 #54 Aug 10 2024 01:29:24
%S A047058 1,6,72,1296,31104,933120,33592320,1410877440,67722117120,
%T A047058 3656994324480,219419659468800,14481697524940800,1042682221795737600,
%U A047058 81329213300067532800,6831653917205672755200,614848852548510547968000
%N A047058 a(n) = 6^n * n!.
%C A047058 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
%C A047058 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
%C A047058 From _Jianing Song_, Mar 29 2021: (Start)
%C A047058 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.
%C A047058 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)
%H A047058 Vincenzo Librandi, <a href="/A047058/b047058.txt">Table of n, a(n) for n = 0..300</a>
%H A047058 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=528">Encyclopedia of Combinatorial Structures 528</a>.
%F A047058 a(n) = A051151(n+1, 0).
%F A047058 E.g.f.: 1/(1 - 6*x).
%F A047058 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
%F A047058 From _Amiram Eldar_, Jun 25 2020: (Start)
%F A047058 Sum_{n>=0} 1/a(n) = e^(1/6) (A092515).
%F A047058 Sum_{n>=0} (-1)^n/a(n) = e^(-1/6) (A092727). (End)
%p A047058 seq( 6^n*n!, n=0..20); # _G. C. Greubel_, Jun 08 2020
%t A047058 Table[6^n n!,{n,0,20}] (* _Harvey P. Dale_, Mar 30 2018 *)
%o A047058 (Magma) [6^n*Factorial(n): n in [0..20]]; // _Vincenzo Librandi_, Oct 05 2011
%Y A047058 Cf. A000142, A000165, A008542, A008543, A047053, A051151, A053103, A092515, A092727.
%K A047058 nonn,easy
%O A047058 0,2
%A A047058 Joe Keane (jgk(AT)jgk.org)
%E A047058 Name changed by _Arkadiusz Wesolowski_, Oct 04 2011