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A244138 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n*(n-1) as Sum(k=0..n)T(n,k)*binomial(n,k). 28

%I

%S 0,0,0,0,0,2,0,0,4,-6,0,0,8,-18,36,0,0,16,-54,144,-320,0,0,32,-162,

%T 576,-1600,3750,0,0,64,-486,2304,-8000,22500,-54432,0,0,128,-1458,

%U 9216,-40000,135000,-381024,941192,0,0,256,-4374,36864,-200000,810000,-2667168,7529536,-18874368

%N Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n*(n-1) as Sum(k=0..n)T(n,k)*binomial(n,k).

%C T(n,k)=k*(1-k)^(k-2)*k^(n-k) for k>1, while T(n,0)=T(n,1)=0 by convention.

%H Stanislav Sykora, <a href="/A244138/b244138.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.(19), with a=1.

%e The first rows of the triangle are:

%e 0,

%e 0, 0,

%e 0, 0, 2,

%e 0, 0, 4, -6,

%e 0, 0, 8, -18, 36,

%e 0, 0, 16, -54, 144, -320,

%e 0, 0, 32, -162, 576, -1600, 3750,

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

%o v = vector((nmax+1)*(nmax+2)/2);v[1]=0;

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

%o for(k=2,n,v[irow+k]=k*(1-k)^(k-2)*k^(n-k);););

%o return(v);}

%o a=seq(100);

%Y Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244139, A244140, A244141, A244142, A244143.

%K sign,tabl

%O 0,6

%A _Stanislav Sykora_, Jun 22 2014

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Last modified November 17 13:12 EST 2019. Contains 329230 sequences. (Running on oeis4.)