%I A007489 M2818
%S A007489 0,1,3,9,33,153,873,5913,46233,409113,4037913,43954713,522956313,
%T A007489 6749977113,93928268313,1401602636313,22324392524313,378011820620313,
%U A007489 6780385526348313,128425485935180313,2561327494111820313,53652269665821260313
%N A007489 Sum of k!, k=1..n.
%C A007489 Equals row sums of triangle A143122 starting (1, 3, 9, 33,...). - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Jul 26 2008
%C A007489 A007489(n) for n>=4 does not yield a perfect square [From Alexander R. 
               Povolotsky (pevnev(AT)juno.com), Oct 16 2008]
%C A007489 Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 14 2009: 
               (Start)
%C A007489 Number of cycles that can be written in the form (j,j+1,j+2,...), in 
               all permutations of {1,2,...,n}. Example: a(3)=9 because in (1)(2)(3), 
               (1)(23), (12)(3), (13)(2), (123), (132) we have 3+2+2+1+1+0=9 such 
               cycles.
%C A007489 (End)
%D A007489 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007489 T. D. Noe, <a href="b007489.txt">Table of n, a(n) for n=0..100</a>
%H A007489 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha132.htm">Factorizations of many number sequences</a>
%H A007489 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha103.htm">Factorizations of many number sequences</a>
%H A007489 Alexsandar Petojevic, <a href="http://www.cs.uwaterloo.ca/journals/JIS/
               index.html">The Function vM_m(s; a; z) and Some Well-Known Sequences</
               a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
%H A007489 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Factorial.html">Link to a section of The World of Mathematics.</a>
%H A007489 G. Xiao, Sigma Server, <a href="http://wims.unice.fr/~wims/en_tool~analysis~sigma.en.html">
               Operate on "n!"</a>
%H A007489 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers</a>
%H A007489 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LeftFactorial.html">Left Factorial</a>
%F A007489 a(n) = Sum[P(n, k) / C(n, k) {k=1...n}] - Ross La Haye (rlahaye(AT)new.rr.com), 
               Sep 21 2004
%F A007489 a(n)=3*A056199(n) for n>=2 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Feb 10 2007
%F A007489 a(n)=!(n+1)+1=A003422(n+1)+1 - Artur Jasinski, Nov 08 2007
%F A007489 Starting (1, 3, 9, 33, 153,...), = row sums of triangle A137593 - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Jan 28 2008
%F A007489 a(n) = a(n-1) + n! for n >= 2. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Jun 16 2009]
%p A007489 A007489 := proc(n) local i; add(i!,i=1..n); end;
%t A007489 FoldList[Plus, 0, (Range@ 21)! ] (* Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Sep 21 2007 *)
%t A007489 Table[Sum[i!, {i, 1, n}], {n, 0, 21}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 12 2009]
%Y A007489 Equals A003422(n+1) - 1.
%Y A007489 Cf. A137593.
%Y A007489 Cf. A143122.
%Y A007489 A161128 [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 14 2009]
%Y A007489 Sequence in context: A012584 A101899 A009220 this_sequence A097677 A138769 
               A100076
%Y A007489 Adjacent sequences: A007486 A007487 A007488 this_sequence A007490 A007491 
               A007492
%K A007489 nonn,easy,nice
%O A007489 0,3
%A A007489 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)