OFFSET
0,5
COMMENTS
Initial term T(0,0) may be computed as 0, depending on formula and convention.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
FORMULA
T(n,k) = k^n * sum(binomial(n,n-k-j),j=0..n-k) = k^n * A055248(n,k-1).
T(n,k) = k^n * binomial(n,n-k) * 2F1(1, k-n; k+1)(-1)
T(n,1) = A000225(n). - R. J. Mathar, Feb 08 2021
EXAMPLE
1
0 1
0 3 4
0 7 32 27
0 15 176 405 256
0 31 832 3888 6144 3125
0 63 3648 30618 90112 109375 46656
0 127 15360 216513 1048576 2265625 2239488 823543
MAPLE
A215079 := proc(n, k)
k^n*add( binomial(n, n-k-j), j=0..n-k) ;
end proc: # R. J. Mathar, Feb 08 2021
MATHEMATICA
Flatten[Table[Table[Sum[k^n*Binomial[n, n - k - j], {j, 0, n - k}], {k, 0, n}], {n, 0, 10}], 1]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Olivier Gérard, Aug 02 2012
STATUS
approved