OFFSET
0,5
COMMENTS
T(n,k)=(-k)^(k-1)*(n+k)^(n-k) for k>0, while T(n,0)=0^n 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.(13), with b=1.
EXAMPLE
The first rows of the triangle are:
1,
0, 1,
0, 3, -2,
0, 16, -10, 9,
0, 125, -72, 63, -64,
0, 1296, -686, 576, -576, 625,
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]=(-k*b)^(k-1)*(n+k*b)^(n-k); ); );
return(v); }
a=seq(100, 1);
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Stanislav Sykora, Jun 22 2014
STATUS
approved