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 A244125 Triangle read by rows: terms T(n,k) of a binomial decomposition of 2^n-1 as Sum(k=0..n)T(n,k). 28
 0, 0, 1, 0, 4, -1, 0, 12, -9, 4, 0, 32, -54, 64, -27, 0, 80, -270, 640, -675, 256, 0, 192, -1215, 5120, -10125, 9216, -3125, 0, 448, -5103, 35840, -118125, 193536, -153125, 46656, 0, 1024, -20412, 229376, -1181250, 3096576, -4287500, 2985984, -823543 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T(n,k)=(1-k)^(k-1)*(1+k)^(n-k)*binomial(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 First rows of the triangle, all summing up to 2^n-1: 1 0 1 0 4  -1 0 12 -9 4 0 32 -54 64 -27 0 80 -270 640 -675 256 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)*binomial(n, k); ); );   return(v); }   a=seq(100, 1) CROSSREFS Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143. Sequence in context: A145880 A048516 A060638 * A007789 A081114 A069018 Adjacent sequences:  A244122 A244123 A244124 * A244126 A244127 A244128 KEYWORD sign,tabl AUTHOR Stanislav Sykora, Jun 21 2014 STATUS approved

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Last modified April 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)