Particular Values of Unsigned Stirling Numbers of the First Kind
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Theorem
This page gathers together some particular values of unsigned Stirling numbers of the first kind.
Unsigned Stirling Number of the First Kind: $\ds {0 \brack n}$
- $\ds {0 \brack n} = \delta_{0 n}$
Unsigned Stirling Number of the First Kind: $\ds {1 \brack n}$
- $\ds {1 \brack n} = \delta_{1 n}$
Unsigned Stirling Number of the First Kind: $\ds {n \brack n}$
- $\ds {n \brack n} = 1$
Unsigned Stirling Number of the First Kind: $\ds {n \brack n - 1}$
- $\ds {n \brack n - 1} = \binom n 2$
Unsigned Stirling Number of the First Kind: $\ds {n \brack n - 2}$
- $\ds {n \brack n - 2} = \binom n 4 + 2 \binom {n + 1} 4$
Unsigned Stirling Number of the First Kind: $\ds {n \brack n - 3}$
- $\ds {n \brack n - 3} = \binom n 6 + 8 \binom {n + 1} 6 + 6 \binom {n + 2} 6$
Unsigned Stirling Number of the First Kind: $\ds {n + 1 \brack 0}$
- $\ds {n + 1 \brack 0} = 0$
Unsigned Stirling Number of the First Kind: $\ds {n + 1 \brack 1}$
- $\ds {n + 1 \brack 1} = n!$