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Faà di Bruno's formula gives an explicit equation for the nth derivative of the composition f(g(t)). If f(t) and g(t) are functions for which all necessary derivatives are ...

A Ferrers diagram represents partitions as patterns of dots, with the nth row having the same number of dots as the nth term in the partition. The spelling "Ferrars" (Skiena ...

In the early 1950s, Ernst Straus asked 1. Is every region illuminable from every point in the region? 2. Is every region illuminable from at least one point in the region? ...

The transformation of a sequence a_1, a_2, ... with a_n=sum_(d|n)b_d (1) into the sequence b_1, b_2, ... via the Möbius inversion formula, b_n=sum_(d|n)mu(n/d)a_d. (2) The ...

The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

For 2<=n<=32, it is possible to select 2n lattice points with x,y in [1,n] such that no three are in a straight line (where "straight line" means any line in the plane--not ...

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

Schmidt (1993) proposed the problem of determining if for any integer r>=2, the sequence of numbers {c_k^((r))}_(k=1)^infty defined by the binomial sums sum_(k=0)^n(n; ...

The simple continued fraction representations of e given by [2; 1, 2, 1, 1, 4, 1, 1, 6, ...] (OEIS A003417). This continued fraction is sometimes known as Euler's continued ...

R. C. Read defined the anarboricity of a graph G as the maximum number of edge-disjoint nonacyclic (i.e., cyclic) subgraphs of G whose union is G (Harary and Palmer 1973, p. ...