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 A244123 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, 8, 0, 9, -90, 108, 0, -16, 576, -2352, 2048, 0, 25, -2800, 28800, -72900, 50000, 0, -36, 11520, -262440, 1440000, -2635380, 1492992, 0, 49, -42336, 1984500, -20870080, 76204800, -109160142, 52706752, 0, -64, 143360, -13172544, 247726080, -1599416000, 4337012736, -5103000000, 2147483648 (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  8 0, 9 -90 108 0 -16 576 -2352 2048 0, 25 -2800 28800 -72900 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)*binomial(n, k); ); );   return(v); }   a=seq(100, -1); CROSSREFS Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143. Sequence in context: A086468 A125507 A198583 * A280652 A104538 A120580 Adjacent sequences:  A244120 A244121 A244122 * A244124 A244125 A244126 KEYWORD sign,tabl AUTHOR Stanislav Sykora, Jun 21 2014 STATUS approved

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Last modified April 11 14:44 EDT 2021. Contains 342886 sequences. (Running on oeis4.)