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A244120 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 A244120 #15 Jun 25 2014 09:38:22
%S A244120 1,0,1,0,2,0,0,3,6,0,0,4,32,12,0,0,5,120,180,20,0,0,6,384,1458,768,30,
%T A244120 0,0,7,1120,9072,12096,2800,42,0,0,8,3072,48600,131072,81000,9216,56,
%U A244120 0,0,9,8064,236196,1152000,1440000,472392,28224,72,0,0,10,20480,1071630,8847360,19531250,13271040,2500470,81920,90,0
%N A244120 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 A244120 T(n,k)=n*(n-k)^(k-1)*k^(n-k) for k>0, while T(n,0)=0^n by convention.
%H A244120 Stanislav Sykora, <a href="/A244120/b244120.txt">Table of n, a(n) for rows 0..100</a>
%H A244120 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.(5), with b=1.
%e A244120 The first rows of the triangle are:
%e A244120 1
%e A244120 0 1
%e A244120 0 2   0
%e A244120 0 3   6   0
%e A244120 0 4  32  12  0
%e A244120 0 5 120 180 20 0
%o A244120 (PARI) seq(nmax,b)={my(v,n,k,irow);
%o A244120   v = vector((nmax+1)*(nmax+2)/2);v[1]=1;
%o A244120   for(n=1,nmax,irow=1+n*(n+1)/2;v[irow]=0;
%o A244120   for(k=1,n,v[irow+k] = n*(n-k*b)^(k-1)*(k*b)^(n-k);););
%o A244120   return(v);}
%o A244120   a=seq(100,1);
%Y A244120 Cf. A244116, A244117, A244118, A244119, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.
%K A244120 nonn,tabl
%O A244120 0,5
%A A244120 _Stanislav Sykora_, Jun 21 2014