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 A244136 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, 1, 2, 0, 4, 2, 9, 0, 27, 8, 9, 64, 0, 256, 54, 36, 64, 625, 0, 3125, 512, 243, 256, 625, 7776, 0, 46656, 6250, 2304, 1728, 2500, 7776, 117649, 0, 823543, 93312, 28125, 16384, 16875, 31104, 117649, 2097152, 0, 16777216, 1647086, 419904, 200000, 160000, 209952, 470596, 2097152, 43046721 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS T(n,k)=(k)^(k-1)*(n-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.(13), with b=-1. EXAMPLE The first rows of the triangle are: 1, 0, 1, 0, 1, 2, 0, 4, 2, 9, 0, 27, 8, 9, 64, 0, 256, 54, 36, 64, 625, 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]=(-k*b)^(k-1)*(n+k*b)^(n-k); ); ); return(v); } a=seq(100, -1); CROSSREFS Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244137, A244138, A244139, A244140, A244141, A244142, A244143. Sequence in context: A327442 A068773 A234312 * A133168 A145382 A192423 Adjacent sequences:  A244133 A244134 A244135 * A244137 A244138 A244139 KEYWORD nonn,tabl AUTHOR Stanislav Sykora, Jun 22 2014 STATUS approved

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Last modified September 21 08:38 EDT 2020. Contains 337268 sequences. (Running on oeis4.)