OFFSET
0,5
COMMENTS
T(n,k)=(1-k)^(k-1)*(1+k)^(n-k)*binomial(n,k) for k>0, while T(n,0)=0 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.(6), with b=1 and a=1.
EXAMPLE
First rows of the triangle, all summing up to 2^n-1:
1
0 1
0 4 -1
0 12 -9 4
0 32 -54 64 -27
0 80 -270 640 -675 256
PROG
(PARI) seq(nmax, b)={my(v, n, k, irow);
v = vector((nmax+1)*(nmax+2)/2); v[1]=0;
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)*(1+k*b)^(n-k)*binomial(n, k); ); );
return(v); }
a=seq(100, 1)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Stanislav Sykora, Jun 21 2014
STATUS
approved