Definition:Stirling's Triangle of the First Kind (Unsigned)

Definition
Stirling's Triangle of the First Kind (Unsigned) is formed by arranging unsigned Stirling numbers of the first kind as follows:


 * $\begin{array}{r|rrrrrrrrrr}

n & \left[{n \atop 0}\right] & \left[{n \atop 1}\right] & \left[{n \atop 2}\right] & \left[{n \atop 3}\right] & \left[{n \atop 4}\right] & \left[{n \atop 5}\right] & \left[{n \atop 6}\right] & \left[{n \atop 7}\right] & \left[{n \atop 8}\right] & \left[{n \atop 9}\right] \\ \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}$

Also see

 * Definition:Stirling Numbers


 * Definition:Stirling's Triangles


 * Definition:Stirling's Triangle of the First Kind (Signed)
 * Definition:Stirling's Triangle of the Second Kind


 * Definition:Pascal's Triangle