[seqfan] re A094645 Generalized Stirling number triangle of first kind.
Meeussen Wouter (bkarnd)
wouter.meeussen at vandemoortele.com
Tue May 15 14:46:11 CEST 2012
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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