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 A244121 Triangle read by rows: terms T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k). 28
 1, 0, 1, 0, 4, 0, 0, 9, 18, 0, 0, 16, 192, 48, 0, 0, 25, 1200, 1800, 100, 0, 0, 36, 5760, 29160, 11520, 180, 0, 0, 49, 23520, 317520, 423360, 58800, 294, 0, 0, 64, 86016, 2721600, 9175040, 4536000, 258048, 448, 0, 0, 81, 290304, 19840464, 145152000, 181440000, 39680928, 1016064, 648, 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)*binomial(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 First rows of the triangle, all summing up to n^n: 1 0 1 0 4   0 0 9  18   0 0 16 192  48  0 0 25 1200 1800 100 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)*binomial(n, k); ); );   return(v); }   a=seq(100, 1); CROSSREFS Cf. A244116, A244117, A244118, A244119, A244120, 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: A127733 A330379 A249035 * A127774 A127319 A272626 Adjacent sequences:  A244118 A244119 A244120 * A244122 A244123 A244124 KEYWORD nonn,tabl AUTHOR Stanislav Sykora, Jun 21 2014 STATUS approved

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Last modified April 10 19:06 EDT 2021. Contains 342853 sequences. (Running on oeis4.)