0,6

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

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.

A. H. Voigt, Theorie der Zahlenreihen und der Reihengleichungen, Leipzig, 1911.

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.

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]

A001118:=-120/(z-1)/(4*z-1)/(3*z-1)/(2*z-1)/(5*z-1); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation. Gives sequence except for 5 leading terms.]

Cf. A001117, A000919, A019538, A000920.

Sequence in context: A027795 A053567 A056270 this_sequence A052767 A110839 A144858

Adjacent sequences: A001115 A001116 A001117 this_sequence A001119 A001120 A001121

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

Extended with formula and alternate description by Christian G. Bower (bowerc(AT)usa.net), Aug 15 1998.