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A000919 4^n-C(4,3)*3^n+C(4,2)*2^n-C(4,1).
(Formerly M5151 N2235)
+0
14
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)
OFFSET

1,4

COMMENT

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

REFERENCES

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.

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.

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.

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

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); [Conjectured by S. Plouffe in his 1992 dissertation.]

CROSSREFS

Cf. A001117, A001118, A019538.

Sequence in context: A052663 A052796 A056269 this_sequence A014340 A052753 A052520

Adjacent sequences: A000916 A000917 A000918 this_sequence A000920 A000921 A000922

KEYWORD

nonn

AUTHOR

njas

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.


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