%I A001118 M5377 N2334
%S A001118 1,0,0,0,0,120,1800,16800,126000,834120,5103000,29607600,165528000,901020120,
%T A001118 4809004200,25292030400,131542866000,678330198120,3474971465400,
%U A001118 17710714165200,89904730860000,454951508208120,2296538629446600
%N A001118 Differences of 0; labeled ordered partitions into 5 parts.
%C A001118 Number of surjections from an n-element set onto a five-element set, 
               with n >= 5. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Dec 15 2007
%D A001118 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001118 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001118 H. T. Davis, Tables of the Mathematical Functions. Vols. 1 and 2, 2nd 
               ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity 
               Univ., San Antonio, TX, Vol. 2, p. 212.
%D A001118 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               33.
%D A001118 J. F. Steffensen, Interpolation, 2nd ed., Chelsea, NY, 1950, see p. 54.
%D A001118 A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Goschen, 
               Leipzig, 1911, p. 31.
%H A001118 A. H. Voigt, <a href="http://historical.library.cornell.edu/cgi-bin/cul.math/
               docviewer?did=05260001&seq=7">Theorie der Zahlenreihen und der Reihengleichungen</
               a>, Leipzig, 1911.
%H A001118 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A001118 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A001118 Sum((-1)^i*binomial(5, i)*(5-i)^n, i = 0 .. 4).
%F A001118 5!*S(n, 5). E.g.f.: (e^x-1)^5.
%F A001118 a(n)=5^n-C(5,4)*4^n+C(5,3)*3^n-C(5,2)*2^n+C(5,1). - Mohamed Bouhamida 
               (bhmd95(AT)yahoo.fr), Dec 15 2007
%F A001118 G.f.:(-1-274*x^4+225*x^3-85*x^2+15*x)/((x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(5*x-1)) 
               [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]
%p A001118 A001118:=-120/(z-1)/(4*z-1)/(3*z-1)/(2*z-1)/(5*z-1); [Conjectured (correctly) 
               by S. Plouffe in his 1992 dissertation. Gives sequence except for 
               5 leading terms.]
%Y A001118 Cf. A001117, A000919, A019538, A000920.
%Y A001118 Sequence in context: A027795 A053567 A056270 this_sequence A052767 A110839 
               A144858
%Y A001118 Adjacent sequences: A001115 A001116 A001117 this_sequence A001119 A001120 
               A001121
%K A001118 nonn,easy
%O A001118 0,6
%A A001118 N. J. A. Sloane (njas(AT)research.att.com).
%E A001118 Extended with formula and alternate description by Christian G. Bower 
               (bowerc(AT)usa.net), Aug 15 1998.