Multiplying a diagonal matrix containing powers of one over rad two by the transpose of the Cholesky decomposition of a matrix of Delannoy numbers gives this object.  
A 1992 paper by Andrew Granville concerns "Zaphod Beeblebrox's Brain" and a certain part of this object.  Multiplying a diagonal matrix containing powers of one over rad two by the transpose of the Cholesky decomposition of a matrix of Delannoy numbers gives this object.  One variant of this object, which can be considered an infinite one-dimensional cellular automaton, is known by a portmanteau word that combines its (*) namesake with Galois.  The earliest known construction of it was by Jia Xian, several centuries before its namesake studied it.  For 10 points, name this structure most commonly used to find the coefficients of binomials to a power, named for a 17th century French mathematician.
A 1992 paper by Andrew Granville concerns "Zaphod Beeblebrox's Brain" and a certain part of this object.  
{Pascal}'s {Triangle} (1) [CM]