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 A244132 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n as Sum(k=0..n)T(n,k)*binomial(n,k). 28
 0, 0, 1, 0, 0, 2, 0, 0, -2, 9, 0, 0, 2, -18, 64, 0, 0, -2, 36, -192, 625, 0, 0, 2, -72, 576, -2500, 7776, 0, 0, -2, 144, -1728, 10000, -38880, 117649, 0, 0, 2, -288, 5184, -40000, 194400, -705894, 2097152, 0, 0, -2, 576, -15552, 160000, -972000, 4235364, -14680064, 43046721 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS T(n,k)=(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.(12), with b=-1. EXAMPLE The first rows of the triangle are: 0, 0, 1, 0, 0, 2, 0, 0, -2, 9, 0, 0, 2, -18, 64, 0, 0, -2, 36, -192, 625, 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]=(-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, A244126, A244127, A244128, A244129, A244130, A244131, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143. Sequence in context: A202496 A165664 A019263 * A337615 A330607 A169776 Adjacent sequences:  A244129 A244130 A244131 * A244133 A244134 A244135 KEYWORD sign,tabl AUTHOR Stanislav Sykora, Jun 22 2014 STATUS approved

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Last modified April 11 14:58 EDT 2021. Contains 342886 sequences. (Running on oeis4.)