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A094294
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a(n) = n*a(n-1) - n + 2 for n > 1; a(1)=1.
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4
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1, 2, 5, 18, 87, 518, 3621, 28962, 260651, 2606502, 28671513, 344058146, 4472755887, 62618582406, 939278736077, 15028459777218, 255483816212691, 4598708691828422, 87375465144740001, 1747509302894800002, 36697695360790800023, 807349297937397600486, 18569033852560144811157
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OFFSET
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1,2
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COMMENTS
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Index of the first occurrence of n in A094293.
For n >= 3, a(n) is also the number of the minimal nonobtuse binary triangulations of the unit n-cube (see Brandts et al. link).
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LINKS
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FORMULA
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a(n+1) = (n+1)*a(n) - n + 1, or a(n) = n*a(n-1) - (n-2). [Corrected by M. F. Hasler, Apr 09 2009]
a(n) = 1 + Sum_{k=2..n} n!/k! = ceiling(n!*(e-2)). - Michel Marcus, Sep 19 2012
Conjecture: (-n+3)*a(n) + (n^2-2*n-2)*a(n-1) - (n-1)*(n-2)*a(n-2) = 0. - R. J. Mathar, Sep 10 2015
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EXAMPLE
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a(1) = 1;
a(2) = 2*a(1) - 0 = 2;
a(3) = 3*a(2) - 1 = 5;
a(4) = 4*a(3) - 2 = 18;
a(5) = 5*a(4) - 3 = 87. (End)
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MAPLE
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option remember;
if n =1 then
1 ;
else
n*procname(n-1)-n+2 ;
end if;
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = n*a[n - 1] - n + 2;
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PROG
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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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EXTENSIONS
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STATUS
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approved
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