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A051189
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Octo-factorial numbers.
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15
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1, 8, 128, 3072, 98304, 3932160, 188743680, 10569646080, 676457349120, 48704929136640, 3896394330931200, 342882701121945600, 32916739307706777600, 3423340888001504870400, 383414179456168545484800
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OFFSET
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0,2
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COMMENTS
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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
Number of n X n monomial matrices whose nonzero entries are unit quaternions.
Number of ways of reassembling n slices of toast or of binding n square pages. - Donald S. McDonald, Sep 24 2005
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LINKS
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FORMULA
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a(n) = 8*A034976(n) = Product_{k=1..n} 8*k, n >= 1; a(0) = 1.
a(n) = n!*8^n.
E.g.f.: 1/(1-8*x).
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
Sum_{n>=0) 1/a(n) = e^(1/8).
Sum_{n>=0) (-1)^n/a(n) = e^(-1/8). (End)
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MATHEMATICA
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PROG
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(SageMath) [8^n*factorial(n) for n in range(40)] # G. C. Greubel, Oct 21 2022
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CROSSREFS
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Shifted absolute values are column 1 of A051187.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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