Derives recursive and closed formulas for moments of waiting times for prescribed words in coin flips and die rolls using one-parameter Eulerian number extensions, Goulden-Jackson cluster method, and Faà di Bruno's formula.
Litt,X-post, March 16 2024,https://x.com/littmath/status/1769044719034647001
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Moments for generalizations of a coin flip game
Derives recursive and closed formulas for moments of waiting times for prescribed words in coin flips and die rolls using one-parameter Eulerian number extensions, Goulden-Jackson cluster method, and Faà di Bruno's formula.