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 A244142 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, 6, -15, 0, 0, 18, -75, 196, 0, 0, 54, -375, 1372, -3645, 0, 0, 162, -1875, 9604, -32805, 87846, 0, 0, 486, -9375, 67228, -295245, 966306, -2599051, 0, 0, 1458, -46875, 470596, -2657205, 10629366, -33787663, 91125000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS T(n,k)=(-1)^k*k*(2*k-1)^(n-2) for k>1, while T(n,0)=0 and T(1,1)=0^(n-1) 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.(21), with a=1, b=2. EXAMPLE The first rows of the triangle are: 0, 0, 1, 0, 0, 2, 0, 0, 6, -15, 0, 0, 18, -75, 196, 0, 0, 54, -375, 1372, -3645 PROG (PARI) seq(nmax)={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; if(n==1, v[irow+1]=1, v[irow+1]=0); for(k=2, n, v[irow+k]=(-1)^k*k*(2*k-1)^(n-2); ); ); return(v); } a=seq(100); CROSSREFS Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244143. Sequence in context: A329290 A244133 A348639 * A161800 A246608 A100344 Adjacent sequences: A244139 A244140 A244141 * A244143 A244144 A244145 KEYWORD sign,tabl AUTHOR Stanislav Sykora, Jun 23 2014 STATUS approved

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Last modified June 12 14:38 EDT 2024. Contains 373331 sequences. (Running on oeis4.)