OFFSET
0,10
FORMULA
T(0,k)=1 and T(n,k) = Sum_{j=0..n} j! * k^(j-1) * Stirling1(n,j) for n > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
-1, 1, 3, 5, 7, 9, ...
2, 2, 14, 38, 74, 122, ...
-6, 4, 86, 384, 1042, 2204, ...
24, 14, 664, 4854, 18344, 49774, ...
MATHEMATICA
T[0, k_] = 1; T[n_, k_] := Sum[If[k == 0 && j <= 1, 1, k^(j - 1)] * j! * StirlingS1[n, j], {j, 0, n}]; Table[T[k, n - k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, May 01 2021 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Jun 12 2020
STATUS
approved