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A244136
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, 1, 2, 0, 4, 2, 9, 0, 27, 8, 9, 64, 0, 256, 54, 36, 64, 625, 0, 3125, 512, 243, 256, 625, 7776, 0, 46656, 6250, 2304, 1728, 2500, 7776, 117649, 0, 823543, 93312, 28125, 16384, 16875, 31104, 117649, 2097152, 0, 16777216, 1647086, 419904, 200000, 160000, 209952, 470596, 2097152, 43046721
OFFSET
0,6
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, 1, 2,
0, 4, 2, 9,
0, 27, 8, 9, 64,
0, 256, 54, 36, 64, 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
nonn,tabl
AUTHOR
Stanislav Sykora, Jun 22 2014
STATUS
approved