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A244138
Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n*(n-1) as Sum(k=0..n)T(n,k)*binomial(n,k).
28
0, 0, 0, 0, 0, 2, 0, 0, 4, -6, 0, 0, 8, -18, 36, 0, 0, 16, -54, 144, -320, 0, 0, 32, -162, 576, -1600, 3750, 0, 0, 64, -486, 2304, -8000, 22500, -54432, 0, 0, 128, -1458, 9216, -40000, 135000, -381024, 941192, 0, 0, 256, -4374, 36864, -200000, 810000, -2667168, 7529536, -18874368
OFFSET
0,6
COMMENTS
T(n,k)=k*(1-k)^(k-2)*k^(n-k) for k>1, while T(n,0)=T(n,1)=0 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.(19), with a=1.
EXAMPLE
The first rows of the triangle are:
0,
0, 0,
0, 0, 2,
0, 0, 4, -6,
0, 0, 8, -18, 36,
0, 0, 16, -54, 144, -320,
0, 0, 32, -162, 576, -1600, 3750,
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; v[irow+1]=0;
for(k=2, n, v[irow+k]=k*(1-k)^(k-2)*k^(n-k); ); );
return(v); }
a=seq(100);
KEYWORD
sign,tabl
AUTHOR
Stanislav Sykora, Jun 22 2014
STATUS
approved