OFFSET
1,5
COMMENTS
T(n,k)=(-k)^(k-1)*k^(n-k) for k>0, while T(n,0)=0 by convention. The flattened triangle start with row 1, coefficient T(1,0).
Resembles A076014, but with added powers of 0, and with sign-alternating columns.
LINKS
Stanislav Sykora, Table of n, a(n) for rows 1..100
S. Sykora, An Abel's Identity and its Corollaries, Stan's Library, Volume V, 2014, DOI 10.3247/SL5Math14.004. See eq.(11), with b=1.
EXAMPLE
The first rows of the triangle (starting at n=1):
0, 1,
0, 1, -2,
0, 1, -4, 9,
0, 1, -8, 27, -64,
0, 1, -16, 81, -256, 625,
0, 1, -32, 243, -1024, 3125, -7776,
PROG
(PARI) seq(nmax, b)={my(v, n, k, irow);
v = vector((nmax+1)*(nmax+2)/2-1);
for(n=1, nmax, irow=n*(n+1)/2; v[irow]=0;
for(k=1, n, v[irow+k]=(-1)^(k-1)*(k*b)^(n-1); ); );
return(v); }
a=seq(100, 1);
CROSSREFS
KEYWORD
sign,tabf
AUTHOR
Stanislav Sykora, Jun 22 2014
STATUS
approved