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A052562
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a(n) = 5^n * n!.
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25
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1, 5, 50, 750, 15000, 375000, 11250000, 393750000, 15750000000, 708750000000, 35437500000000, 1949062500000000, 116943750000000000, 7601343750000000000, 532094062500000000000, 39907054687500000000000
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OFFSET
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0,2
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COMMENTS
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A simple regular expression in a labeled universe.
For n >= 1 a(n) is the order of the wreath product of the symmetric group S_n and the Abelian group (C_5)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001
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LINKS
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FORMULA
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a(n) = A051150(n+1, 0) (first column of triangle).
E.g.f.: 1/(1-5*x).
a(n) = 5*n*a(n-1) with a(0)=1.
G.f.: 1/(1-5*x/(1-5*x/(1-10*x/(1-10*x/(1-15*x/(1-15*x/(1-20*x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012
G.f.: 1/Q(0), where Q(k) = 1 - 5*x*(2*k+1) - 25*x^2*(k+1)^2/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Sep 28 2013
Sum_{n>=0) 1/a(n) = e^(1/5) (A092514).
Sum_{n>=0) (-1)^n/a(n) = e^(-1/5) (A092618). (End)
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MAPLE
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spec := [S, {S=Sequence(Union(Z, Z, Z, Z, Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
with(combstruct):A:=[N, {N=Cycle(Union(Z$5))}, labeled]: seq(count(A, size=n)/5, n=1..16); # Zerinvary Lajos, Dec 05 2007
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MATHEMATICA
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PROG
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(Sage) [5^n*factorial(n) for n in (0..20)] # G. C. Greubel, May 05 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Joe Keane (jgk(AT)jgk.org)
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EXTENSIONS
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STATUS
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approved
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