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A244134 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k)*binomial(n,k).

%I A244134 #9 Jun 25 2014 09:41:30
%S A244134 1,0,1,0,3,-2,0,16,-10,9,0,125,-72,63,-64,0,1296,-686,576,-576,625,0,
%T A244134 16807,-8192,6561,-6400,6875,-7776,0,262144,-118098,90000,-85184,
%U A244134 90000,-101088,117649,0,4782969,-2000000,1449459,-1327104,1373125,-1524096,1764735,-2097152
%N A244134 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k)*binomial(n,k).
%C A244134 T(n,k)=(-k)^(k-1)*(n+k)^(n-k) for k>0, while T(n,0)=0^n by convention.
%H A244134 Stanislav Sykora, <a href="/A244134/b244134.txt">Table of n, a(n) for rows 0..100</a>
%H A244134 S. Sykora, <a href="http://dx.doi.org/10.3247/SL5Math14.004">An Abel's Identity and its Corollaries</a>, Stan's Library, Volume V, 2014, DOI 10.3247/SL5Math14.004. See eq.(13), with b=1.
%e A244134 The first rows of the triangle are:
%e A244134 1,
%e A244134 0, 1,
%e A244134 0, 3, -2,
%e A244134 0, 16, -10, 9,
%e A244134 0, 125, -72, 63, -64,
%e A244134 0, 1296, -686, 576, -576, 625,
%o A244134 (PARI) seq(nmax,b)={my(v,n,k,irow);
%o A244134 v = vector((nmax+1)*(nmax+2)/2);v[1]=1;
%o A244134 for(n=1,nmax,irow=1+n*(n+1)/2;v[irow]=0;
%o A244134   for(k=1,n,v[irow+k]=(-k*b)^(k-1)*(n+k*b)^(n-k);););
%o A244134 return(v);}
%o A244134 a=seq(100,1);
%Y A244134 Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.
%K A244134 sign,tabl
%O A244134 0,5
%A A244134 _Stanislav Sykora_, Jun 22 2014