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A244122
Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k)*binomial(n,k).
28
1, 0, 1, 0, -2, 8, 0, 3, -30, 108, 0, -4, 96, -588, 2048, 0, 5, -280, 2880, -14580, 50000, 0, -6, 768, -13122, 96000, -439230, 1492992, 0, 7, -2016, 56700, -596288, 3628800, -15594306, 52706752, 0, -8, 5120, -235224, 3538944, -28561000, 154893312, -637875000, 2147483648, 0
OFFSET
0,5
COMMENTS
T(n,k)=n*(n+k)^(k-1)*(-k)^(n-k) for k>0, while T(n,0)=0^n 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.(5), with b=-1.
EXAMPLE
The first rows of the triangle are:
1
0 1
0 -2 8
0 3 -30 108
0 -4 96 -588 2048
0 5 -280 2880 -14580 50000
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] = n*(n-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