Particular Values of Signed Stirling Numbers of the First Kind
Jump to navigation
Jump to search
Theorem
This page gathers together some particular values of signed Stirling numbers of the first kind.
Signed Stirling Number of the First Kind: $\map s {0, n}$
- $\map s {0, n} = \delta_{0 n}$
Signed Stirling Number of the First Kind: $\map s {1, n}$
- $\map s {1, n} = \delta_{1 n}$
Signed Stirling Number of the First Kind: $\map s {n, n}$
- $\map s {n, n} = 1$
Signed Stirling Number of the First Kind: $\map s {n, n - 1}$
- $\map s {n, n - 1} = -\dbinom n 2$
Signed Stirling Number of the First Kind: $\map s {n + 1, 0}$
- $\map s {n + 1, 0} = 0$
Signed Stirling Number of the First Kind: $\map s {n + 1, 1}$
- $\map s {n + 1, 1} = \paren {-1}^n n!$