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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).

%I A244138 #8 Jun 25 2014 09:42:43
%S A244138 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 A244138 576,-1600,3750,0,0,64,-486,2304,-8000,22500,-54432,0,0,128,-1458,
%U A244138 9216,-40000,135000,-381024,941192,0,0,256,-4374,36864,-200000,810000,-2667168,7529536,-18874368
%N 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).
%C A244138 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 A244138 Stanislav Sykora, <a href="/A244138/b244138.txt">Table of n, a(n) for rows 0..100</a>
%H A244138 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 A244138 The first rows of the triangle are:
%e A244138 0,
%e A244138 0, 0,
%e A244138 0, 0, 2,
%e A244138 0, 0, 4, -6,
%e A244138 0, 0, 8, -18, 36,
%e A244138 0, 0, 16, -54, 144, -320,
%e A244138 0, 0, 32, -162, 576, -1600, 3750,
%o A244138 (PARI) seq(nmax)={my(v,n,k,irow);
%o A244138 v = vector((nmax+1)*(nmax+2)/2);v[1]=0;
%o A244138 for(n=1,nmax,irow=1+n*(n+1)/2;v[irow]=0;v[irow+1]=0;
%o A244138   for(k=2,n,v[irow+k]=k*(1-k)^(k-2)*k^(n-k);););
%o A244138 return(v);}
%o A244138 a=seq(100);
%Y A244138 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 A244138 sign,tabl
%O A244138 0,6
%A A244138 _Stanislav Sykora_, Jun 22 2014