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Home » The Ultimate Guide to Genshin Characters: Which Heroes Will Define Your Next Adventure? - Carbonext

The Ultimate Guide to Genshin Characters: Which Heroes Will Define Your Next Adventure? - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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The value of $S(5,3)$ is computed as follows:
We use the recurrence: $S(n,k) = k \cdot S(n-1,k) + S(n-1,k-1)$
With base cases:
$S(n,1) = 1$ for $n \geq 1$
$S(n,n) = 1$
$S(n,0) = 0$ for $n > 0$
$S(2,2) = 1$
$S(3,2) = 2 \cdot S(2,2) + S(2,1) = 2 \cdot 1 + 1 = 3$
$S(3,3) = 1$
$S(4,2) = 2 \cdot S(3,2) + S(3,1) = 2 \cdot 3 + 1 = 7$

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