OFFSET
0,5
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k) = 1 if k = 0 or k = n, otherwise 5*n*k*(n-k)*(n^2 -n*k +k^2).
T(n, n-k) = T(n, k).
Sum_{k=0..n} T(n, k) = 2 - [n=0] + 30*A006858(n).
From G. C. Greubel, Dec 13 2021: (Start)
T(n, 1) = [n<2] + 30*A006325(n).
T(2*n, n) = [n=0] + 30*A000584(n). (End)
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 30, 1;
1, 210, 210, 1;
1, 780, 960, 780, 1;
1, 2100, 2850, 2850, 2100, 1;
1, 4650, 6720, 7290, 6720, 4650, 1;
1, 9030, 13650, 15540, 15540, 13650, 9030, 1;
1, 15960, 24960, 29400, 30720, 29400, 24960, 15960, 1;
1, 26280, 42210, 51030, 54900, 54900, 51030, 42210, 26280, 1;
1, 40950, 67200, 82950, 91200, 93750, 91200, 82950, 67200, 40950, 1;
MATHEMATICA
T[n_, k_]:= If[n*k*(n-k)==0, 1, n^5 - (k^5 + (n-k)^5)];
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten
PROG
(Magma)
A157634:= func< n, k | k eq 0 or k eq n select 1 else n^5 - (k^5 + (n-k)^5) >;
[A157634(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Dec 13 2021
(Sage)
def A157634(n, k): return 1 if (k==0 or k==n) else n^5 - (k^5 + (n-k)^5)
flatten([[A157634(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Dec 13 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Mar 03 2009
STATUS
approved