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A244136 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 A244136 #8 Jun 25 2014 09:42:12
%S A244136 1,0,1,0,1,2,0,4,2,9,0,27,8,9,64,0,256,54,36,64,625,0,3125,512,243,
%T A244136 256,625,7776,0,46656,6250,2304,1728,2500,7776,117649,0,823543,93312,
%U A244136 28125,16384,16875,31104,117649,2097152,0,16777216,1647086,419904,200000,160000,209952,470596,2097152,43046721
%N A244136 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 A244136 T(n,k)=(k)^(k-1)*(n-k)^(n-k) for k>0, while T(n,0)=0^n by convention.
%H A244136 Stanislav Sykora, <a href="/A244136/b244136.txt">Table of n, a(n) for rows 0..100</a>
%H A244136 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 A244136 The first rows of the triangle are:
%e A244136 1,
%e A244136 0, 1,
%e A244136 0, 1, 2,
%e A244136 0, 4, 2, 9,
%e A244136 0, 27, 8, 9, 64,
%e A244136 0, 256, 54, 36, 64, 625,
%o A244136 (PARI) seq(nmax, b)={my(v, n, k, irow);
%o A244136 v = vector((nmax+1)*(nmax+2)/2); v[1]=1;
%o A244136 for(n=1, nmax, irow=1+n*(n+1)/2; v[irow]=0;
%o A244136   for(k=1, n, v[irow+k]=(-k*b)^(k-1)*(n+k*b)^(n-k); ); );
%o A244136 return(v); }
%o A244136 a=seq(100,-1);
%Y A244136 Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244137, A244138, A244139, A244140, A244141, A244142, A244143.
%K A244136 nonn,tabl
%O A244136 0,6
%A A244136 _Stanislav Sykora_, Jun 22 2014