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The sporadic groups are the 26 finite simple groups that do not fit into any of the four infinite families of finite simple groups (i.e., the cyclic groups of prime order, ...

sum_(k=0)^dr_k^B(d-k)!x^k=sum_(k=0)^d(-1)^kr_k^(B^_)(d-k)!x^k(x+1)^(d-k).

Take any positive integer of two digits or more, reverse the digits, and add to the original number. This is the operation of the reverse-then-add sequence. Now repeat the ...

Q(n), also denoted q(n) (Abramowitz and Stegun 1972, p. 825), gives the number of ways of writing the integer n as a sum of positive integers without regard to order with the ...

Let c_k be the number of edge covers of a graph G of size k. Then the edge cover polynomial E_G(x) is defined by E_G(x)=sum_(k=0)^mc_kx^k, (1) where m is the edge count of G ...

A geometric series sum_(k)a_k is a series for which the ratio of each two consecutive terms a_(k+1)/a_k is a constant function of the summation index k. The more general case ...

A polygonal number and 6-polygonal number of the form n(2n-1). The first few are 1, 6, 15, 28, 45, ... (OEIS A000384). The generating function for the hexagonal numbers is ...

A theorem, also known as Bachet's conjecture, which Bachet inferred from a lack of a necessary condition being stated by Diophantus. It states that every positive integer can ...

The negadecimal representation of a number n is its representation in base -10 (i.e., base negative 10). It is therefore given by the coefficients a_na_(n-1)...a_1a_0 in n = ...

A nexus number is a figurate number built up of the nexus of cells less than n steps away from a given cell. The nth d-dimensional nexus number is given by N_d(n) = ...