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A000920
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Differences of 0: 6!*S(n,6).
(Formerly M5473 N2370)
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8
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0, 0, 0, 0, 0, 720, 15120, 191520, 1905120, 16435440, 129230640, 953029440, 6711344640, 45674188560, 302899156560, 1969147121760, 12604139926560, 79694820748080, 499018753280880, 3100376804676480, 19141689213218880, 117579844328562000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| 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
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REFERENCES
| 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.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 33.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. F. Steffensen, Interpolation, 2nd ed., Chelsea, NY, 1950, see p. 54.
A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Goschen, Leipzig, 1911, p. 31.
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LINKS
| A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Leipzig, 1911.
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FORMULA
| Sum((-1)^i*binomial(6, i)*(6-i)^n, i = 0 .. 5).
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
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]
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MAPLE
| 720/(-1+z)/(6*z-1)/(4*z-1)/(3*z-1)/(2*z-1)/(5*z-1);
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
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CROSSREFS
| Cf. A001117, A000919, A019538, A000920.
Cf. A000918, A000919, A001117, A001118.
Sequence in context: A004033 A137891 A056271 * A052779 A037212 A126781
Adjacent sequences: A000917 A000918 A000919 * A000921 A000922 A000923
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
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