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A number of the form Tt_n=((n+2; 2); 2)=1/8n(n+1)(n+2)(n+3) (Comtet 1974, Stanley 1999), where (n; k) is a binomial coefficient. The first few values are 3, 15, 45, 105, 210, ...

The twin composites may be defined by analogy with the twin primes as pairs of composite numbers (n,n+2). Since all even number are trivially twin composites, it is natural ...

Let P_i=x_i:y_i:z_i be trilinear points for i=1, 2, 3. The A-vertex of the unary cofactor triangle is then defined as the point y_2z_3-z_2y_3:z_2x_3-x_2z_3:x_2y_3-y_2x_3, and ...

A characterization of normal spaces which states that a topological space X is normal iff, for any two nonempty closed disjoint subsets A, and B of X, there is a continuous ...

A walk is a sequence v_0, e_1, v_1, ..., v_k of graph vertices v_i and graph edges e_i such that for 1<=i<=k, the edge e_i has endpoints v_(i-1) and v_i (West 2000, p. 20). ...

If at least one of d, e, or f has the form q^(-N) for some nonnegative integer N (in which case both sums terminate after N+1 terms), then ...

The notion of weak amenability was first introduced by Bade et al. (1987), who termed a commutative Banach algebra A "weakly amenable" if every continuous derivation from A ...

The pathological function f_a(x)=sum_(k=1)^infty(sin(pik^ax))/(pik^a) (originally defined for a=2) that is continuous but differentiable only on a set of points of measure ...

In the Wolfram Language, WignerD[{j, m ,n}, psi, theta, phi] gives the m×n matrix element of a (2j+1)-dimensional unitary representation of SU(2) parametrized by three Euler ...

Let V be a real symmetric matrix of large order N having random elements v_(ij) that for i<=j are independently distributed with equal densities, equal second moments m^2, ...