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 A244119 Triangle read by rows: terms of a binomial decomposition of 1 as Sum(k=0..n)T(n,k). 29
 1, 0, 1, 0, -2, 3, 0, 3, -18, 16, 0, -4, 72, -192, 125, 0, 5, -240, 1440, -2500, 1296, 0, -6, 720, -8640, 30000, -38880, 16807, 0, 7, -2016, 45360, -280000, 680400, -705894, 262144, 0, -8, 5376, -217728, 2240000, -9072000, 16941456, -14680064, 4782969 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T(n,k)=(1+k)^(k-1)*(-k)^(n-k)*binomial(n,k) for k>0, while T(n,0)=0^n by convention. Sequence A161628, arising from a different context, appears to be the same, but with opposite signs of odd rows. 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 First rows of the triangle, all summing up to 1: 1 0  1 0 -2    3 0  3  -18   16 0 -4   72 -192   125 0  5 -240 1440 -2500 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)*binomial(n, k); );   ); return(v); }   a=seq(100, -1); CROSSREFS Cf. A161628, A244116, A244117, A244118, 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: A137663 A257740 A161628 * A122059 A164917 A166238 Adjacent sequences:  A244116 A244117 A244118 * A244120 A244121 A244122 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.)