OFFSET
0,6
COMMENTS
T(n,k) = (1+k)^(k-1)*(-k)^(n-k) for k>0, where T(n,0) = 0^n.
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
The first rows of the triangle are:
1
0 1
0 -1 3
0 1 -6 16
0 -1 12 -48 125
0 1 -24 144 -500 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); );
); return(v); }
a=seq(100, -1);
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Stanislav Sykora, Jun 21 2014
STATUS
approved