OFFSET
1,6
FORMULA
T(n,k) = Sum_{j=1..n} Stirling1(n,j) * T(j,k-1), k>1, T(n,1) = (n-1)!.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 0, -1, -2, -3, -4, ...
2, 1, 3, 8, 16, 27, ...
6, -1, -13, -48, -124, -259, ...
24, 8, 77, 386, 1270, 3244, ...
120, -26, -576, -3905, -16243, -50375, ...
MATHEMATICA
T[n_, 1] := (n - 1)!; T[n_, k_] := T[n, k] = Sum[StirlingS1[n, j] * T[j, k - 1], {j, 1, n}]; Table[T[k, n - k + 1], {n, 1, 10}, {k, 1, n}] // Flatten (* Amiram Eldar, Feb 11 2022 *)
PROG
(PARI) T(n, k) = if(k==1, (n-1)!, sum(j=1, n, stirling(n, j, 1)*T(j, k-1)));
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Feb 11 2022
STATUS
approved