1,4

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

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.

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.

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

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.]

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

nonn

njas