login
A244118
Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 1 as Sum_{k=0..n} T(n,k)*binomial(n,k).
28
1, 0, 1, 0, -1, 3, 0, 1, -6, 16, 0, -1, 12, -48, 125, 0, 1, -24, 144, -500, 1296, 0, -1, 48, -432, 2000, -6480, 16807, 0, 1, -96, 1296, -8000, 32400, -100842, 262144, 0, -1, 192, -3888, 32000, -162000, 605052, -1835008, 4782969, 0, 1, -384, 11664, -128000, 810000, -3630312, 12845056, -38263752, 100000000
OFFSET
0,6
COMMENTS
T(n,k) = (1+k)^(k-1)*(-k)^(n-k) for k>0, where T(n,0) = 0^n.
LINKS
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);
KEYWORD
sign,tabl
AUTHOR
Stanislav Sykora, Jun 21 2014
STATUS
approved