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 A244118 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, 3, 0, 1, -6, 16, 0, -1, 12, -48, 125, 0, 1, -24, 144, -500, 1296, 0, -1, 48, -432, 2000, -6480, 16807, 0, 1, -96, 1296, -8000, 32400, -100842, 262144, 0, -1, 192, -3888, 32000, -162000, 605052, -1835008, 4782969, 0, 1, -384, 11664, -128000, 810000, -3630312, 12845056, -38263752, 100000000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS T(n,k)=(1+k)^(k-1)*(-k)^(n-k) for k>0, while T(n,0)=0^n. 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.(4), with b=-1. EXAMPLE The first rows of the triangle are: 1 0  1 0 -1   3 0  1  -6  16 0 -1  12 -48  125 0  1 -24 144 -500 1296 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. A244116, A244117, 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: A143397 A341856 A339350 * A273155 A208345 A216807 Adjacent sequences:  A244115 A244116 A244117 * A244119 A244120 A244121 KEYWORD sign,tabl AUTHOR Stanislav Sykora, Jun 21 2014 STATUS approved

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Last modified April 11 14:29 EDT 2021. Contains 342886 sequences. (Running on oeis4.)