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 A244122 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
 1, 0, 1, 0, -2, 8, 0, 3, -30, 108, 0, -4, 96, -588, 2048, 0, 5, -280, 2880, -14580, 50000, 0, -6, 768, -13122, 96000, -439230, 1492992, 0, 7, -2016, 56700, -596288, 3628800, -15594306, 52706752, 0, -8, 5120, -235224, 3538944, -28561000, 154893312, -637875000, 2147483648, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T(n,k)=n*(n+k)^(k-1)*(-k)^(n-k) for k>0, while T(n,0)=0^n by convention. LINKS Stanislav Sykora, Table of n, a(n) for rows 0..100 S. Sykora, An Abel's Identity and its Corollaries, Stan's Library, Volume V, 2014, DOI 10.3247/SL5Math14.004. See eq.(5), with b=-1. EXAMPLE The first rows of the triangle are: 1 0  1 0 -2    8 0  3  -30  108 0 -4   96 -588   2048 0  5 -280 2880 -14580 50000 PROG (PARI) seq(nmax, b)={my(v, n, k, irow);   v = vector((nmax+1)*(nmax+2)/2); v[1]=1;   for(n=1, nmax, irow=1+n*(n+1)/2; v[irow]=0;   for(k=1, n, v[irow+k] = n*(n-k*b)^(k-1)*(k*b)^(n-k); ); );   return(v); }   a=seq(100, -1); CROSSREFS Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143. Sequence in context: A016593 A020818 A197252 * A021785 A136664 A086728 Adjacent sequences:  A244119 A244120 A244121 * A244123 A244124 A244125 KEYWORD sign,tabl AUTHOR Stanislav Sykora, Jun 21 2014 STATUS approved

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Last modified April 10 19:18 EDT 2021. Contains 342853 sequences. (Running on oeis4.)