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 A244116 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 1 as Sum_{k=0..n} T(n,k)*binomial(n,k). 28
 1, 0, 1, 0, 1, -1, 0, 1, -2, 4, 0, 1, -4, 12, -27, 0, 1, -8, 36, -108, 256, 0, 1, -16, 108, -432, 1280, -3125, 0, 1, -32, 324, -1728, 6400, -18750, 46656, 0, 1, -64, 972, -6912, 32000, -112500, 326592, -823543, 0, 1, -128, 2916, -27648, 160000, -675000, 2286144, -6588344, 16777216 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS T(n,k) = (1-k)^(k-1) * k^(n-k) for k>0, while T(n,0) = 0^n by convention. LINKS Stanislav Sykora, Table of n, rows 0..100 S. Sykora, An Abel's Identity and its Corollaries, Stan's Library, Volume V, 2014. See eq.(4) with b=1. EXAMPLE The first few rows of the triangle are:   1   0 1   0 1 -1   0 1 -2 4   0 1 -4 12  -27   0 1 -8 36 -108 256   ... 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] = (1-k*b)^(k-1)*(k*b)^(n-k); );   ); return(v); }   a=seq(100, 1); CROSSREFS Cf. A244117, A244118, A244119, A244120, 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: A309148 A226031 A308460 * A138133 A302937 A005657 Adjacent sequences:  A244113 A244114 A244115 * A244117 A244118 A244119 KEYWORD sign,tabl AUTHOR Stanislav Sykora, Jun 21 2014 STATUS approved

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Last modified April 14 22:47 EDT 2021. Contains 342971 sequences. (Running on oeis4.)