Search: id:A014288
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%I A014288
%S A014288 0,1,2,5,17,77,437,2957,23117,204557,2018957,21977357,261478157,
%T A014288 3374988557,46964134157,700801318157,11162196262157,189005910310157,
%U A014288 3390192763174157,64212742967590157,1280663747055910157
%N A014288 [ Sum k!/2, k=0..n ], or floor( A003422(n+1)/2 ).
%C A014288 The first term a(0) would be a fraction if the floor( ... ) function 
               would be omitted ; for n>=2, all terms from A003422 are even. - M. 
               F. Hasler, Dec 16 2007
%F A014288 a(1)=1, a(2)=2, a(n)=(n+1)*a(n-1)-n*a(n-2). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Sep 07 2002
%F A014288 a(0) = 0, a(n) = (1/2)*Floor[1+1*Floor[1+2*Floor[1+....+(n-1)*Floor[1+n*Floor[1]]]....]. 
               [From Joseph E. Cooper III (easonrevant(AT)gmail.com), Aug 19 2008]
%t A014288 Contribution from Joseph E. Cooper III (easonrevant(AT)gmail.com), Aug 
               19 2008: (Start)
%t A014288 f[x_] := {Floor[1 + (n - x[[2]])*x[[1]]], x[[2]] + 1}
%t A014288 Nest[f, {1, 0}, n][[1]]/2 (End)
%o A014288 (PARI) A014288(n)=sum(k=0,n,k!)>>1 \\ - M. F. Hasler, Dec 16 2007
%Y A014288 Cf. A003422, A067078, A007489.
%Y A014288 Sequence in context: A118100 A129591 A099825 this_sequence A020096 A054499 
               A001186
%Y A014288 Adjacent sequences: A014285 A014286 A014287 this_sequence A014289 A014290 
               A014291
%K A014288 nonn
%O A014288 0,3
%A A014288 N. J. A. Sloane (njas(AT)research.att.com).
%E A014288 Edited by M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 16 2007

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