OFFSET
0,9
COMMENTS
T(n,k) = (1-k)^(k-1) * k^(n-k) for k>0, and T(n,0) = 0^n by convention.
LINKS
Stanislav Sykora, Table of n, rows 0..100
S. Sykora, An Abel's Identity and its Corollaries, Stan's Library, Volume V, 2014. See eq.(4) with b=1.
EXAMPLE
The first few rows of the triangle are:
1
0 1
0 1 -1
0 1 -2 4
0 1 -4 12 -27
0 1 -8 36 -108 256
...
MAPLE
A244116 := (n, j) -> (-1)^(j + 1) * j^(n - j) * (j - 1)^(j - 1):
for n from 0 to 9 do seq(A244116(n, k), k = 0..n) od; # Peter Luschny, Jan 28 2023
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