A177974 Triangle T(n,k) = n!/(n - k)! + n!/k! - n! read by rows, 0 <= k <= n.
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 0, 4, 1, 1, 5, -40, -40, 5, 1, 1, 6, -330, -480, -330, 6, 1, 1, 7, -2478, -3990, -3990, -2478, 7, 1, 1, 8, -20104, -33264, -36960, -33264, -20104, 8, 1, 1, 9, -181368, -301896, -344736, -344736, -301896, -181368, 9, 1
Offset: 0
Examples
Triangle begins: 1; 1, 1; 1, 2, 1; 1, 3, 3, 1; 1, 4, 0, 4, 1; 1, 5, -40, -40, 5, 1; 1, 6, -330, -480, -330, 6, 1; 1, 7, -2478, -3990, -3990, -2478, 7, 1; 1, 8, -20104, -33264, -36960, -33264, -20104, 8, 1; 1, 9, -181368, -301896, -344736, -344736, -301896, -181368, 9, 1; ...
Links
- Seiichi Manyama, Rows n = 0..139, flattened
Crossrefs
Cf. A155162.
Programs
-
Mathematica
Flatten[Table[Table[n!/(n - k)! + n!/k! - n!, {k, 0, n}], {n, 0, 10}]]
Formula
T(n,k) = n!/(n - k)! + n!/k! - n.
T(n,k) = A155162(n,k) - n!. - Seiichi Manyama, Sep 26 2023