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 A244120 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, 0, 0, 3, 6, 0, 0, 4, 32, 12, 0, 0, 5, 120, 180, 20, 0, 0, 6, 384, 1458, 768, 30, 0, 0, 7, 1120, 9072, 12096, 2800, 42, 0, 0, 8, 3072, 48600, 131072, 81000, 9216, 56, 0, 0, 9, 8064, 236196, 1152000, 1440000, 472392, 28224, 72, 0, 0, 10, 20480, 1071630, 8847360, 19531250, 13271040, 2500470, 81920, 90, 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   0 0 3   6   0 0 4  32  12  0 0 5 120 180 20 0 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, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143. Sequence in context: A064146 A336309 A336255 * A277536 A269159 A216394 Adjacent sequences:  A244117 A244118 A244119 * A244121 A244122 A244123 KEYWORD nonn,tabl AUTHOR Stanislav Sykora, Jun 21 2014 STATUS approved

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Last modified April 10 18:17 EDT 2021. Contains 342853 sequences. (Running on oeis4.)