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A051189 Octo-factorial numbers.

%I A051189 #56 Aug 12 2024 01:28:02
%S A051189 1,8,128,3072,98304,3932160,188743680,10569646080,676457349120,
%T A051189 48704929136640,3896394330931200,342882701121945600,
%U A051189 32916739307706777600,3423340888001504870400,383414179456168545484800
%N A051189 Octo-factorial numbers.
%C A051189 For n >= 1, a(n) is the order of the wreath product of the symmetric group S_n and the Abelian group (C_8)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001
%C A051189 Number of n X n monomial matrices whose nonzero entries are unit quaternions.
%C A051189 Number of ways of reassembling n slices of toast or of binding n square pages. - _Donald S. McDonald_, Sep 24 2005
%H A051189 Vincenzo Librandi, <a href="/A051189/b051189.txt">Table of n, a(n) for n = 0..300</a>
%H A051189 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A051189 a(n) = 8*A034976(n) = Product_{k=1..n} 8*k, n >= 1; a(0) = 1.
%F A051189 a(n) = n!*8^n.
%F A051189 E.g.f.: 1/(1-8*x).
%F A051189 G.f.: 1/(1 - 8*x/(1 - 8*x/(1 - 16*x/(1 - 16*x/(1 - 24*x/(1 - 24*x/(1 - 32*x/(1 - 32*x/(1 - ... (continued fraction). - _Philippe Deléham_, Jan 07 2012
%F A051189 From _Amiram Eldar_, Jun 25 2020: (Start)
%F A051189 Sum_{n>=0} 1/a(n) = e^(1/8).
%F A051189 Sum_{n>=0} (-1)^n/a(n) = e^(-1/8). (End)
%t A051189 Table[n! 8^n,{n,0,20}] (* _Harvey P. Dale_, Aug 14 2021 *)
%o A051189 (Magma) [8^n*Factorial(n): n in [0..20]]; // _Vincenzo Librandi_, Oct 05 2011
%o A051189 (SageMath) [8^n*factorial(n) for n in range(40)] # _G. C. Greubel_, Oct 21 2022
%Y A051189 Cf. A000165, A034976, A047058, A051188, A053115.
%Y A051189 Shifted absolute values are column 1 of A051187.
%K A051189 easy,nonn
%O A051189 0,2
%A A051189 _Wolfdieter Lang_