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

Neil Sloane njasloane at gmail.com
Tue May 15 18:06:54 CEST 2012


It's not obvious to me - so please add it as a conjecture (or of
course a theorem if you have a proof)
Neil

On Tue, May 15, 2012 at 8:46 AM, Meeussen Wouter (bkarnd) <
wouter.meeussen at vandemoortele.com> wrote:

> 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.
>
>
> --------------------
> 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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-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



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