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Polynomials O_n(x) that can be defined by the sum O_n(x)=1/4sum_(k=0)^(|_n/2_|)(n(n-k-1)!)/(k!)(1/2x)^(2k-n-1) (1) for n>=1, where |_x_| is the floor function. They obey the ...

A polygonal number of the form N_n=n(7n-5)/2, also called an enneagonal number. The first few are 1, 9, 24, 46, 75, 111, 154, 204, ... (OEIS A001106). The generating function ...

A set in which no element divides the sum of any nonempty subset of the other elements. For example, {2,3,5} is dividing, since 2|(3+5) (and 5|(2+3)), but {4,6,7} is ...

An odd number is an integer of the form n=2k+1, where k is an integer. The odd numbers are therefore ..., -3, -1, 1, 3, 5, 7, ... (OEIS A005408), which are also the gnomonic ...

The Pell polynomials P(x) are the W-polynomials generated by the Lucas polynomial sequence using the generator p(x)=2x, q(x)=1. This gives recursive equations for P(x) from ...

A figurate number which is constructed as a centered cube with a square pyramid appended to each face, RhoDod_n = CCub_n+6P_(n-1)^((4)) (1) = (2n-1)(2n^2-2n+1), (2) where ...

The hyperbolic sine integral, often called the "Shi function" for short, is defined by Shi(z)=int_0^z(sinht)/tdt. (1) The function is implemented in the Wolfram Language as ...

A figurate number of the form StOct_n = O_n+8Te_(n-1) (1) = n(2n^2-1), (2) where O_n is an octahedral number and Te_n is a tetrahedral number. The first few are 1, 14, 51, ...

The superfactorial of n is defined by Pickover (1995) as n$=n!^(n!^(·^(·^(·^(n!)))))_()_(n!). (1) The first two values are 1 and 4, but subsequently grow so rapidly that 3$ ...

A figurate number constructed by taking the (3n-2)th tetrahedral number and removing the (n-1)th tetrahedral number from each of the four corners, Ttet_n = ...