Search: id:A000920
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%I A000920 M5473 N2370
%S A000920 0,0,0,0,0,720,15120,191520,1905120,16435440,129230640,953029440,6711344640,
%T A000920 45674188560,302899156560,1969147121760,12604139926560,79694820748080,
%U A000920 499018753280880,3100376804676480,19141689213218880,117579844328562000
%N A000920 Differences of 0: 6!*S(n,6).
%C A000920 Number of surjections from an n-element set onto a six-element set, with 
               n >= 6. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Dec 15 2007
%D A000920 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000920 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000920 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 A000920 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               33.
%D A000920 J. F. Steffensen, Interpolation, 2nd ed., Chelsea, NY, 1950, see p. 54.
%D A000920 A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Goschen, 
               Leipzig, 1911, p. 31.
%H A000920 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 A000920 Sum((-1)^i*binomial(6, i)*(6-i)^n, i = 0 .. 5).
%F A000920 a(n)=6^n-C(6,5)*5^n+C(6,4)*4^n-C(6,3)*3^n+C(6,2)*2^n-C(6,1) with n>=6. 
               - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Dec 15 2007
%F A000920 G.f.:(720*x^6)/((x-1)*(6*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 A000920 720/(-1+z)/(6*z-1)/(4*z-1)/(3*z-1)/(2*z-1)/(5*z-1);
%p A000920 with (combstruct):ZL:=[S,{S=Sequence(U,card=r),U=Set(Z,card>=1)}, labeled]: 
               seq(count(subs(r=6,ZL),size=m),m=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 09 2007
%Y A000920 Cf. A001117, A000919, A019538, A000920.
%Y A000920 Cf. A000918, A000919, A001117, A001118.
%Y A000920 Sequence in context: A004033 A137891 A056271 this_sequence A052779 A037212 
               A126781
%Y A000920 Adjacent sequences: A000917 A000918 A000919 this_sequence A000921 A000922 
               A000923
%K A000920 nonn
%O A000920 1,6
%A A000920 N. J. A. Sloane (njas(AT)research.att.com).
%E A000920 G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, 
               Sep 16 2009.

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