%I A000919 M5151 N2235
%S A000919 0,0,0,24,240,1560,8400,40824,186480,818520,3498000,14676024,60780720,
               249401880,
%T A000919 1016542800,4123173624,16664094960,67171367640,270232006800,1085570781624,
%U A000919 4356217681200,17466686971800,69992221794000,280345359228024,1122510953731440
%N A000919 4^n-C(4,3)*3^n+C(4,2)*2^n-C(4,1).
%C A000919 Differences of 0: 4!*S(n,4).
%C A000919 Number of functions from an n-element set onto a four-element set. - 
               David Wasserman (dwasserm(AT)earthlink.net), Jun 06 2007
%D A000919 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000919 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000919 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 A000919 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               33.
%D A000919 J. F. Steffensen, Interpolation, 2nd ed., Chelsea, NY, 1950, see p. 54.
%D A000919 A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Goschen, 
               Leipzig, 1911, p. 31.
%H A000919 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 A000919 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.
%H A000919 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.
%F A000919 G.f.: 24x^3/[(1-x)(1-2x)(1-3x)(1-4x)].
%F A000919 a(n) = 4^n-binomial(4,3)*3^n+binomial(4,2)*2^n-binomial(4,1) = 24*A000453(n). 
               - David Wasserman (dwasserm(AT)earthlink.net), Jun 06 2007
%F A000919 E.g.f.:(exp(x)-1)^4 [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Feb 11 2009]
%F A000919 For n>=4: a(n+1)=4*a(n)+4*[3^n-3*2^n+3]=4*a(n)+4*A001117(n) [From Geoffrey 
               Critzer (critzer.geoffrey(AT)usd443.org), Feb 27 2009]
%p A000919 with (combstruct):ZL:=[S,{S=Sequence(U,card=r),U=Set(Z,card>=1)}, labeled]: 
               seq(count(subs(r=4,ZL),size=m),m=1..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 09 2007
%p A000919 A000919:=24/(z-1)/(3*z-1)/(2*z-1)/(4*z-1); [S. Plouffe in his 1992 dissertation.]
%Y A000919 Cf. A001117, A001118, A019538.
%Y A000919 Sequence in context: A167548 A052796 A056269 this_sequence A014340 A052753 
               A052520
%Y A000919 Adjacent sequences: A000916 A000917 A000918 this_sequence A000920 A000921 
               A000922
%K A000919 nonn
%O A000919 1,4
%A A000919 N. J. A. Sloane (njas(AT)research.att.com).