[seqfan] re A094645 Generalized Stirling number triangle of first kind.

[Meeussen Wouter (bkarnd)]

hi all,

1;
-1,  1;
0, -1,  1;
0, -1,  0,  1;
0, -2, -1,  2,  1;
0, -6, -5,  5,  5, 1;
0,-24,-26, 15, 25, 9, 1;

I suppose it is quite self evident that the dot product of row n
 with vector (0,1,..,n)  equals (n-1)!
        5 th row:
        (0,-6,-5,5,5,1) . (0,1,2,3,4,5) = 24

If it isn't, then I'll add a comment to that effect.

Wouter.


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Table[CoefficientList[(t-1)*Sum[(-1)^(n+1+m) t^(m-1)  StirlingS1[n+1,m],{m,n+1}],t] ,{n,0,6}];
# . Range[Length[#]]&  /@  %
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