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A094294 a(n) = n*a(n-1) - n + 2 for n > 1; a(1)=1. 4
1, 2, 5, 18, 87, 518, 3621, 28962, 260651, 2606502, 28671513, 344058146, 4472755887, 62618582406, 939278736077, 15028459777218, 255483816212691, 4598708691828422, 87375465144740001, 1747509302894800002, 36697695360790800023, 807349297937397600486, 18569033852560144811157 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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).
LINKS
Jan Brandts, Sander Dijkhuis, Vincent de Haan, and Michal Křížek, There are only two nonobtuse binary triangulations of the unit n-cube, arXiv:1209.3875 [math.CO] and Comput. Geom. 46 (2013) 286.
FORMULA
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
EXAMPLE
From M. F. Hasler, Apr 09 2009: (Start)
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)
MAPLE
A094294 := proc(n)
option remember;
if n =1 then
1 ;
else
n*procname(n-1)-n+2 ;
end if;
end proc: # R. J. Mathar, Feb 06 2016
MATHEMATICA
a[1] = 1; a[n_] := a[n] = n*a[n - 1] - n + 2;
Array[a, 23] (* Jean-François Alcover, Dec 14 2017 *)
PROG
(PARI) A094294(n)={ local(a=1); for( k=2, n, a=k*a-k+2); a } \\ M. F. Hasler, Apr 09 2009
CROSSREFS
Sequence in context: A109995 A142153 A287227 * A005500 A020025 A113715
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Apr 28 2004
EXTENSIONS
Edited, corrected and extended by M. F. Hasler, Apr 09 2009
STATUS
approved

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Last modified June 18 14:18 EDT 2024. Contains 373481 sequences. (Running on oeis4.)