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A000919
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4^n-C(4,3)*3^n+C(4,2)*2^n-C(4,1).
(Formerly M5151 N2235)
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12
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0, 0, 0, 24, 240, 1560, 8400, 40824, 186480, 818520, 3498000, 14676024, 60780720, 249401880, 1016542800, 4123173624, 16664094960, 67171367640, 270232006800, 1085570781624, 4356217681200, 17466686971800, 69992221794000, 280345359228024, 1122510953731440
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Differences of 0: 4!*S(n,4).
Number of functions from an n-element set onto a four-element set. - David Wasserman (dwasserm(AT)earthlink.net), Jun 06 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
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Leipzig, 1911.
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FORMULA
| G.f.: 24x^3/((1-x)(1-2x)(1-3x)(1-4x)).
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
E.g.f.:(exp(x)-1)^4 [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Feb 11 2009]
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]
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MAPLE
| 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
A000919:=24/(z-1)/(3*z-1)/(2*z-1)/(4*z-1); [S. Plouffe in his 1992 dissertation.]
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CROSSREFS
| Cf. A001117, A001118, A019538.
Sequence in context: A192849 A052796 A056269 * A014340 A052753 A052520
Adjacent sequences: A000916 A000917 A000918 * A000920 A000921 A000922
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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