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Search: id:A000919
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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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+0
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; listen)
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OFFSET
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1,4
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COMMENT
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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
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
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
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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
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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
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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
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Cf. A001117, A001118, A019538.
Adjacent sequences: A000916 A000917 A000918 this_sequence A000920 A000921 A000922
Sequence in context: A052663 A052796 A056269 this_sequence A014340 A052753 A052520
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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