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A094294 a(n) = n*a(n-1) - n + 2 for n > 1; a(1)=1.

%I A094294 #30 Jun 16 2019 08:07:56
%S A094294 1,2,5,18,87,518,3621,28962,260651,2606502,28671513,344058146,
%T A094294 4472755887,62618582406,939278736077,15028459777218,255483816212691,
%U A094294 4598708691828422,87375465144740001,1747509302894800002,36697695360790800023,807349297937397600486,18569033852560144811157
%N A094294 a(n) = n*a(n-1) - n + 2 for n > 1; a(1)=1.
%C A094294 Index of the first occurrence of n in A094293.
%C A094294 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).
%H A094294 Jan Brandts, Sander Dijkhuis, Vincent de Haan, and Michal Křížek, <a href="http://arxiv.org/abs/1209.3875">There are only two nonobtuse binary triangulations of the unit n-cube</a>, arXiv:1209.3875 [math.CO] and Comput. Geom. 46 (2013) 286.
%F A094294 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]
%F A094294 a(n) = 1 + Sum_{k=2..n} n!/k! = ceiling(n!*(e-2)). - _Michel Marcus_, Sep 19 2012
%F A094294 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
%e A094294 From _M. F. Hasler_, Apr 09 2009: (Start)
%e A094294 a(1) = 1;
%e A094294 a(2) = 2*a(1) - 0 =  2;
%e A094294 a(3) = 3*a(2) - 1 =  5;
%e A094294 a(4) = 4*a(3) - 2 = 18;
%e A094294 a(5) = 5*a(4) - 3 = 87. (End)
%p A094294 A094294 := proc(n)
%p A094294     option remember;
%p A094294     if n =1 then
%p A094294         1 ;
%p A094294     else
%p A094294         n*procname(n-1)-n+2 ;
%p A094294     end if;
%p A094294 end proc: # _R. J. Mathar_, Feb 06 2016
%t A094294 a[1] = 1; a[n_] := a[n] = n*a[n - 1] - n + 2;
%t A094294 Array[a, 23] (* _Jean-François Alcover_, Dec 14 2017 *)
%o A094294 (PARI) A094294(n)={ local(a=1); for( k=2,n, a=k*a-k+2); a } \\ _M. F. Hasler_, Apr 09 2009
%Y A094294 Cf. A001511, A094293.
%K A094294 nonn,easy
%O A094294 1,2
%A A094294 _Amarnath Murthy_, Apr 28 2004
%E A094294 Edited, corrected and extended by _M. F. Hasler_, Apr 09 2009