login
A244139
Triangle read by rows: terms T(n,k) of a binomial decomposition of n*(n-1) as Sum(k=0..n)T(n,k).
28
0, 0, 0, 0, 0, 2, 0, 0, 12, -6, 0, 0, 48, -72, 36, 0, 0, 160, -540, 720, -320, 0, 0, 480, -3240, 8640, -9600, 3750, 0, 0, 1344, -17010, 80640, -168000, 157500, -54432, 0, 0, 3584, -81648, 645120, -2240000, 3780000, -3048192, 941192, 0, 0, 9216, -367416, 4644864, -25200000, 68040000, -96018048, 67765824, -18874368
OFFSET
0,6
COMMENTS
T(n,k)=k*(1-k)^(k-2)*k^(n-k)*binomial(n,k) for k>1, while T(n,0)=T(n,1)=0 by convention.
LINKS
S. Sykora, An Abel's Identity and its Corollaries, Stan's Library, Volume V, 2014, DOI 10.3247/SL5Math14.004. See eq.(19), with a=1.
EXAMPLE
First rows of the triangle, all summing up to n*(n-1):
0,
0, 0,
0, 0, 2,
0, 0, 12, -6,
0, 0, 48, -72, 36,
0, 0, 160, -540, 720, -320,
0, 0, 480, -3240, 8640, -9600, 3750,
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; v[irow+1]=0;
for(k=2, n, v[irow+k]=k*(1-k)^(k-2)*k^(n-k)*binomial(n, k); ); );
return(v); }
a=seq(100);
KEYWORD
sign,tabl
AUTHOR
Stanislav Sykora, Jun 22 2014
STATUS
approved