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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). 28

%I

%S 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 256,625,7776,0,46656,6250,2304,1728,2500,7776,117649,0,823543,93312,

%U 28125,16384,16875,31104,117649,2097152,0,16777216,1647086,419904,200000,160000,209952,470596,2097152,43046721

%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="/A244136/b244136.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, 1, 2,

%e 0, 4, 2, 9,

%e 0, 27, 8, 9, 64,

%e 0, 256, 54, 36, 64, 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, A244134, A244135, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

%K nonn,tabl

%O 0,6

%A _Stanislav Sykora_, Jun 22 2014

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Last modified April 14 22:46 EDT 2021. Contains 342970 sequences. (Running on oeis4.)