A244134 - OEIS

%I #9 Jun 25 2014 09:41:30

%S 1,0,1,0,3,-2,0,16,-10,9,0,125,-72,63,-64,0,1296,-686,576,-576,625,0,

%T 16807,-8192,6561,-6400,6875,-7776,0,262144,-118098,90000,-85184,

%U 90000,-101088,117649,0,4782969,-2000000,1449459,-1327104,1373125,-1524096,1764735,-2097152

%N 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 T(n,k)=(-k)^(k-1)*(n+k)^(n-k) for k>0, while T(n,0)=0^n by convention.

%H Stanislav Sykora, <a href="/A244134/b244134.txt">Table of n, a(n) for rows 0..100</a>

%H 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 The first rows of the triangle are:

%e 1,

%e 0, 1,

%e 0, 3, -2,

%e 0, 16, -10, 9,

%e 0, 125, -72, 63, -64,

%e 0, 1296, -686, 576, -576, 625,

%o (PARI) seq(nmax,b)={my(v,n,k,irow);

%o v = vector((nmax+1)*(nmax+2)/2);v[1]=1;

%o for(n=1,nmax,irow=1+n*(n+1)/2;v[irow]=0;

%o   for(k=1,n,v[irow+k]=(-k*b)^(k-1)*(n+k*b)^(n-k);););

%o return(v);}

%o a=seq(100,1);

%Y 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 sign,tabl

%O 0,5

%A _Stanislav Sykora_, Jun 22 2014