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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
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
Sequence in context: A329290 A244133 A348639 * A161800 A246608 A100344
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.)