Four Numerical Triangles in Nexus
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Len Smiley  
Three wellknown combinatorial number triangles are tightly related to each other as coefficients in transforms of a seminal sequence of exponential generating functions (for n^{n+m}). A fourth triangle is a part of the picture in much the same way that the "forgotten symmetric functions" adhere to the complete, the monomial, and the power sums. Also, CarlitzRiordan Identities (with tables for Secondorder Eulerian and Secondorder Stirling numbers), Gessel and Stanley multiset permutations (GSPermutations), Golliwog Numbers (featuring tables and a formula for the numbers called "differences of reciprocal powers of unity"), Pez story problem, and Completion of a Sequence of Carlitz.  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Problems/Puzzles 
Math Topics:  Combinatorics, Triangles and Other Polygons, Sequences and Sets 
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