“Euler's Triangle”的概念、定义、习题解题方法及翻译-数学辞典

单词

Euler's Triangle

释义

Euler's Triangle

The triangle of numbers given by

and the Recurrence Relation

for

, where

are Eulerian Numbers.

The numbers 1, 1, 1, 1, 4, 1, 1, 11, 11, 1, ... are Sloane's A008292. Amazingly, the Z-Transform of

are generators for Euler's triangle.

See also Clark's Triangle, Eulerian Number, Leibniz Harmonic Triangle, Number Triangle,Pascal's Triangle, Seidel-Entringer-Arnold Triangle, Z-Transform

References

Sloane, N. J. A. Sequence A008292in ``The On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.

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