OFFSET
0,4
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k) = (n-k)^n - n*k*(n-k) + k^n, with T(0, 0) = 1.
T(n, n-k) = T(n, k).
EXAMPLE
Triangle begins as:
1;
1, 1;
4, 0, 4;
27, 3, 3, 27;
256, 70, 16, 70, 256;
3125, 1005, 245, 245, 1005, 3125;
46656, 15596, 4112, 1404, 4112, 15596, 46656;
MATHEMATICA
T[n_, k_]= If[n==0, 1, k^n +(n-k)^n -n*k*(n-k)];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Magma)
[n eq 0 select 1 else (n-k)^n - n*k*(n-k) + k^n: k in [0..n], n in [0..12]]; // G. C. Greubel, Apr 26 2024
(SageMath)
flatten([[(n-k)^n - n*k*(n-k) + k^n - int(n==0) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Apr 26 2024
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Jun 08 2007
EXTENSIONS
Edited by G. C. Greubel, Apr 26 2024
STATUS
approved