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 A244126 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 2^n-1 as Sum(k=0..n)T(n,k)*binomial(n,k). 28
 0, 0, 1, 0, 0, 3, 0, 0, -3, 16, 0, 0, 3, -32, 125, 0, 0, -3, 64, -375, 1296, 0, 0, 3, -128, 1125, -5184, 16807, 0, 0, -3, 256, -3375, 20736, -84035, 262144, 0, 0, 3, -512, 10125, -82944, 420175, -1572864, 4782969, 0, 0, -3, 1024, -30375, 331776, -2100875, 9437184, -33480783, 100000000, 0, 0, 3, -2048, 91125, -1327104, 10504375, -56623104, 234365481, -800000000, 2357947691, 0, 0, -3, 4096, -273375, 5308416, -52521875 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS T(n,k)=(1+k)^(k-1)*(1-k)^(n-k) for k>0, while T(n,0)=0 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.(6), with b=-1 and a=1. EXAMPLE The first rows of the triangle are: 0, 0, 1, 0, 0, 3, 0, 0, -3, 16, 0, 0, 3, -32, 125, 0, 0, -3, 64, -375, 1296, PROG (PARI) seq(nmax, b)={my(v, n, k, irow);   v = vector((nmax+1)*(nmax+2)/2); v[1]=0;   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)*(1+k*b)^(n-k); ); );   return(v); }   a=seq(100, -1) CROSSREFS Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143. Sequence in context: A079209 A279368 A021773 * A133109 A130208 A288654 Adjacent sequences:  A244123 A244124 A244125 * A244127 A244128 A244129 KEYWORD sign,tabl AUTHOR Stanislav Sykora, Jun 21 2014 STATUS approved

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Last modified December 16 07:12 EST 2018. Contains 318158 sequences. (Running on oeis4.)