Particular Values of Stirling Numbers of the Second Kind
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Theorem
This page gathers together some particular values of Stirling numbers of the second kind.
Stirling Number of the Second Kind: $\ds {0 \brace n}$
- $\ds {0 \brace n} = \delta_{0 n}$
Stirling Number of the Second Kind: $\ds {1 \brace n}$
- $\ds {1 \brace n} = \delta_{1 n}$
Stirling Number of the Second Kind: $\ds {n \brace n}$
- $\ds {n \brace n} = 1$
Stirling Number of the Second Kind: $\ds {n \brace n - 1}$
- $\ds {n \brace n - 1} = \binom n 2$
Stirling Number of the Second Kind: $\ds {n \brace n - 2}$
- $\ds {n \brace n - 2} = \binom {n + 1} 4 + 2 \binom n 4$
Stirling Number of the Second Kind: $\ds {n \brace n - 3}$
- $\ds {n \brace n - 3} = \binom {n + 2} 6 + 8 \binom {n + 1} 6 + 6 \binom n 6$
Stirling Number of the Second Kind: $\ds {n + 1 \brace 0}$
- $\ds {n + 1 \brace 0} = 0$
Stirling Number of the Second Kind: $\ds {n + 1 \brace 1}$
- $\ds {n + 1 \brace 1} = 1$
Stirling Number of the Second Kind: $\ds {n + 1 \brace 2}$
- $\ds {n + 1 \brace 2} = 2^n - 1$