OFFSET
0,6
COMMENTS
T(n,k)=(-1)^k*k*(2*k-1)^(n-2)*binomial(n,k) for k>1, while T(n,0)=0 and T(1,1)=0^(n-1) 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.(21), with a=1, b=2.
EXAMPLE
First rows of the triangle, all summing up to n:
0,
0, 1,
0, 0, 2,
0, 0, 18, -15,
0, 0, 108, -300, 196,
0, 0, 540, -3750, 6860, -3645,
PROG
(PARI) seq(nmax)={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; if(n==1, v[irow+1]=1, v[irow+1]=0);
for(k=2, n, v[irow+k]=(-1)^k*k*(2*k-1)^(n-2)*binomial(n, k); ); );
return(v); }
a=seq(100);
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Stanislav Sykora, Jun 23 2014
STATUS
approved