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A001118
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Differences of 0; labeled ordered partitions into 5 parts.
(Formerly M5377 N2334)
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12
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1, 0, 0, 0, 0, 120, 1800, 16800, 126000, 834120, 5103000, 29607600, 165528000, 901020120, 4809004200, 25292030400, 131542866000, 678330198120, 3474971465400, 17710714165200, 89904730860000, 454951508208120, 2296538629446600
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OFFSET
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0,6
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COMMENTS
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Number of surjections from an n-element set onto a five-element set, with n >= 5. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Dec 15 2007
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REFERENCES
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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
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Leipzig, 1911.
_Simon 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.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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Sum((-1)^i*binomial(5, i)*(5-i)^n, i = 0 .. 4).
5!*S(n, 5). E.g.f.: (e^x-1)^5.
a(n)=5^n-C(5,4)*4^n+C(5,3)*3^n-C(5,2)*2^n+C(5,1). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Dec 15 2007
G.f.:(-1-274*x^4+225*x^3-85*x^2+15*x)/((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
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A001118:=-120/(z-1)/(4*z-1)/(3*z-1)/(2*z-1)/(5*z-1); [Conjectured (correctly) by Simon Plouffe in his 1992 dissertation. Gives sequence except for 5 leading terms.]
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MATHEMATICA
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CoefficientList[Series[(-1-274*x^4+225*x^3-85*x^2+15*x)/((x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(5*x-1)), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 11 2012 *)
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CROSSREFS
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Cf. A001117, A000919, A019538, A000920.
Sequence in context: A223427 A053567 A056270 * A052767 A110839 A219720
Adjacent sequences: A001115 A001116 A001117 * A001119 A001120 A001121
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Extended with formula and alternate description by Christian G. Bower, Aug 15 1998.
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STATUS
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approved
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