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If C_1, C_2, ...C_r are sets of positive integers and union _(i=1)^rC_i=Z^+, then some C_i contains arbitrarily long arithmetic progressions. The conjecture was proved by van ...

The bead-sorting algorithm orders a list of a positive integers increasingly by representing numbers as a list of a 1s, where each 1 stands for a bead. The k initial integers ...

A benzenoid is a fusene that is a subgraph of the regular hexagonal lattice (i.e., a simply connected polyhex). The numbers of n-hexagon benzenoids for n=1, 2, ... are 1, 1, ...

A number defined by b_n=b_n(0), where b_n(x) is a Bernoulli polynomial of the second kind (Roman 1984, p. 294), also called Cauchy numbers of the first kind. The first few ...

Polynomials b_n(x) which form a Sheffer sequence with g(t) = t/(e^t-1) (1) f(t) = e^t-1, (2) giving generating function sum_(k=0)^infty(b_k(x))/(k!)t^k=(t(t+1)^x)/(ln(1+t)). ...

11 21 3 41 4 7 81 5 11 15 161 6 16 26 31 32 (1) The number triangle illustrated above (OEIS A008949) composed of the partial sums of binomial coefficients, a_(nk) = ...

Krall and Fink (1949) defined the Bessel polynomials as the function y_n(x) = sum_(k=0)^(n)((n+k)!)/((n-k)!k!)(x/2)^k (1) = sqrt(2/(pix))e^(1/x)K_(-n-1/2)(1/x), (2) where ...

In floating-point arithmetic, a biased exponent is the result of adding some constant (called the bias) to the exponent chosen to make the range of the exponent nonnegative. ...

A tree (also called a bicentral tree) having two nodes that are graph centers. The numbers of bicentered trees on n=1, 2, ... nodes are 0, 1, 0, 1, 1, 3, 4, 11, 20, 51, 108 ...

A binary bracketing is a bracketing built up entirely of binary operations. The number of binary bracketings of n letters (Catalan's problem) are given by the Catalan numbers ...