Question 3 Let Ak be the number of partitions P of the set {1,2,...n+ 1} such that {k+1} € P but for allj>k+1, {j} ¢ P. 1. Compute A11. 2. Show that An.n is the nth Bell number B(n).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Question 3 Let Ak be the number of partitions P of the set {1,2,...n + 1}
such that {k+ 1} € P but for allj>k+1, {j} ¢ P.
1. Compute A1,1.
2. Show that An.n is the nth Bell number B(n).
Transcribed Image Text:Question 3 Let Ak be the number of partitions P of the set {1,2,...n + 1} such that {k+ 1} € P but for allj>k+1, {j} ¢ P. 1. Compute A1,1. 2. Show that An.n is the nth Bell number B(n).
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