Definition:Stirling's Triangle of the First Kind (Signed)
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Definition
Stirling's Triangle of the First Kind (Signed) is formed by arranging signed Stirling numbers of the first kind as follows:
$\begin{array}{r|rrrrrrrrrr}
n & s(n,0) & s(n,1) & s(n,2) & s(n,3) & s(n,4) & s(n,5) & s(n,6) & s(n,7) & s(n,8) & s(n,9) \\
\hline
0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
2 & 0 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
3 & 0 & 2 & -3 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\
4 & 0 & -6 & 11 & -6 & 1 & 0 & 0 & 0 & 0 & 0 \\
5 & 0 & 24 & -50 & 35 & -10 & 1 & 0 & 0 & 0 & 0 \\
6 & 0 & -120 & 274 & -225 & 85 & -15 & 1 & 0 & 0 & 0 \\
7 & 0 & 720 & -1764 & 1624 & -735 & 175 & -21 & 1 & 0 & 0 \\
8 & 0 & -5040 & 13068 & -13132 & 6769 & -1960 & 322 & -28 & 1 & 0 \\
9 & 0 & 40320 & −109584 & 118124 & −67284 & 22449 & −4536 & 546 & −36 & 1 \\
\end{array}$
This sequence is A008275 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Also see
- Definition:Stirling's Triangle of the First Kind (Unsigned)
- Definition:Stirling's Triangle of the Second Kind
Compare with
Source of Name
This entry was named for James Stirling.
