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A244134
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, 3, -2, 0, 16, -10, 9, 0, 125, -72, 63, -64, 0, 1296, -686, 576, -576, 625, 0, 16807, -8192, 6561, -6400, 6875, -7776, 0, 262144, -118098, 90000, -85184, 90000, -101088, 117649, 0, 4782969, -2000000, 1449459, -1327104, 1373125, -1524096, 1764735, -2097152
OFFSET
0,5
COMMENTS
T(n,k)=(-k)^(k-1)*(n+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.(13), with b=1.
EXAMPLE
The first rows of the triangle are:
1,
0, 1,
0, 3, -2,
0, 16, -10, 9,
0, 125, -72, 63, -64,
0, 1296, -686, 576, -576, 625,
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]=(-k*b)^(k-1)*(n+k*b)^(n-k); ); );
return(v); }
a=seq(100, 1);
KEYWORD
sign,tabl
AUTHOR
Stanislav Sykora, Jun 22 2014
STATUS
approved